Depends how bare-bones you're going, starting from a 'base' Ubuntu (no GUI):
mate-desktop- the absolute minimum (bring your own apps, almost DIY)-
mate-desktop-environment- for a comfortable OS (calculator, file manager, screensaver, etc) 
ubuntu-mate-core- equivalent to the Minimal install option.- That brings the things that makes Ubuntu MATE, Ubuntu MATE (artwork, printer support, ayatana indicators, arctica greeter)
-
ubuntu-mate-desktopequivalent to the Full install option.- That adds everything else like Firefox (snap), LibreOffice, accessibility, etc.
You're probably looking for ubuntu-mate-core, or the "Minimal" install option.
If you went bare bones with mate-desktop, all you get is:
[user@a1001ef60882 ~]$ mate-
mate-about mate-color-select
But it depends: For space saving? Or more like an optimised "from scratch, just what I need" kind of thing?
If you did go with a minimal mate-desktop with Ubuntu MATE configuration, then you might want ubuntu-mate-default-settings, but I'm not sure how that'll play out with almost nothing and a configuration seeking indicators that cannot be found.
Quick test using the Ubuntu Docker image (26.04, 'latest') - similar to a mini ISO.
Obviously in a containerised environment, I can't test the desktop environment, but package wise, this is what it'll install:
mate-desktop (+781 MB)
[user@a1001ef60882 ~]$ sudo apt install mate-desktop
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
The following additional packages will be installed:
adwaita-icon-theme alsa-topology-conf alsa-ucm-conf aspell aspell-en at-spi2-common at-spi2-core
bsdextrautils bubblewrap dbus dbus-bin dbus-daemon dbus-session-bus-common
dbus-system-bus-common dbus-user-session dconf-gsettings-backend dconf-service
dictionaries-common dmsetup docbook-xml emacsen-common enchant-2 fontconfig fontconfig-config
fonts-dejavu-core fonts-dejavu-mono fuse3 gir1.2-girepository-2.0 gir1.2-glib-2.0
glib-networking glib-networking-common glib-networking-services groff-base
gsettings-desktop-schemas gstreamer1.0-gl gstreamer1.0-plugins-base gstreamer1.0-plugins-good
gstreamer1.0-x gtk-update-icon-cache hicolor-icon-theme humanity-icon-theme hunspell-en-us
iso-codes libaa1 libargon2-1 libasound2-data libasound2t64 libaspell15 libasyncns0
libatk-bridge2.0-0t64 libatk1.0-0t64 libatomic1 libatspi2.0-0t64 libavahi-client3
libavahi-common-data libavahi-common3 libavc1394-0 libcaca0 libcairo-gobject2 libcairo2
libcap2-bin libcdparanoia0 libcolord2 libcryptsetup12 libcups2t64 libdatrie1 libdbus-1-3
libdconf1 libdeflate0 libdevmapper1.02.1 libdrm-amdgpu1 libdrm-common libdrm-intel1 libdrm2
libduktape207 libdv4t64 libdw1t64 libegl-mesa0 libegl1 libelf1t64 libenchant-2-2 libepoxy0
libevdev2 libfdisk1 libflac12t64 libfontconfig1 libfreetype6 libfribidi0 libfuse3-3 libgbm1
libgdk-pixbuf-2.0-0 libgdk-pixbuf2.0-bin libgdk-pixbuf2.0-common libgirepository-1.0-1 libgl1
libgl1-mesa-dri libgles2 libglib2.0-0t64 libglib2.0-data libglvnd0 libglx-mesa0 libglx0 libgpm2
libgraphene-1.0-0 libgraphite2-3 libgstreamer-gl1.0-0 libgstreamer-plugins-base1.0-0
libgstreamer-plugins-good1.0-0 libgstreamer1.0-0 libgtk-3-0t64 libgtk-3-bin libgtk-3-common
libgudev-1.0-0 libhandy-1-0 libharfbuzz-icu0 libharfbuzz0b libhunspell-1.7-0 libhyphen0 libicu74
libiec61883-0 libjavascriptcoregtk-4.1-0 libjbig0 libjpeg-turbo8 libjpeg8 libjson-c5
libjson-glib-1.0-0 libjson-glib-1.0-common libkmod2 liblcms2-2 liblerc4 libllvm20
libmanette-0.2-0 libmate-desktop-2-17t64 libmp3lame0 libmpg123-0t64 libncurses6 libnss-systemd
libogg0 libopus0 liborc-0.4-0t64 libpam-cap libpam-systemd libpango-1.0-0 libpangocairo-1.0-0
libpangoft2-1.0-0 libpciaccess0 libpipeline1 libpipewire-0.3-0t64 libpipewire-0.3-common
libpixman-1-0 libpng16-16t64 libproxy1v5 libpulse0 libpython3-stdlib libpython3.12-minimal
libpython3.12-stdlib libraw1394-11 libreadline8t64 librsvg2-2 librsvg2-common libsecret-1-0
libsecret-common libsensors-config libsensors5 libsharpyuv0 libshout3 libslang2 libsndfile1
libsoup-3.0-0 libsoup-3.0-common libspa-0.2-modules libspeex1 libsqlite3-0
libstartup-notification0 libsystemd-shared libtag1v5 libtag1v5-vanilla libtext-iconv-perl
libthai-data libthai0 libtheora0 libtiff6 libtwolame0 libuchardet0 libunwind8 libv4l-0t64
libv4lconvert0t64 libvisual-0.4-0 libvorbis0a libvorbisenc2 libvpx9 libvulkan1 libwavpack1
libwayland-client0 libwayland-cursor0 libwayland-egl1 libwayland-server0 libwebkit2gtk-4.1-0
libwebp7 libwebpdemux2 libwebpmux3 libwebrtc-audio-processing1 libwoff1 libx11-xcb1
libxcb-dri3-0 libxcb-glx0 libxcb-present0 libxcb-randr0 libxcb-render0 libxcb-shm0 libxcb-sync1
libxcb-util1 libxcb-xfixes0 libxcomposite1 libxcursor1 libxdamage1 libxfixes3 libxi6
libxinerama1 libxkbcommon0 libxml2 libxrandr2 libxrender1 libxshmfence1 libxslt1.1 libxtst6
libxv1 libxxf86vm1 libyelp0 lsb-release man-db mate-desktop-common mate-user-guide media-types
mesa-libgallium mesa-vulkan-drivers networkd-dispatcher python3 python3-dbus python3-distro
python3-gi python3-minimal python3.12 python3.12-minimal readline-common session-migration
sgml-base sgml-data shared-mime-info systemd systemd-dev systemd-resolved systemd-sysv
systemd-timesyncd tzdata ubuntu-mono x11-common xdg-dbus-proxy xdg-desktop-portal
xdg-desktop-portal-gtk xdg-user-dirs xkb-data xml-core yelp yelp-xsl
Suggested packages:
aspell-doc spellutils wordlist docbook docbook-dsssl docbook-xsl docbook-defguide groff gvfs
hunspell openoffice.org-hunspell | openoffice.org-core isoquery alsa-utils libasound2-plugins
colord cups-common libdv-bin oss-compat libenchant-2-voikko low-memory-monitor gpm
libvisual-0.4-plugins gstreamer1.0-tools liblcms2-utils opus-tools pciutils pipewire pulseaudio
libraw1394-doc librsvg2-bin lm-sensors speex gstreamer1.0-libav gstreamer1.0-plugins-bad
gstreamer1.0-alsa apparmor www-browser mate-desktop-environment iw | wireless-tools python3-doc
python3-tk python3-venv python-dbus-doc python3.12-venv python3.12-doc binutils binfmt-support
readline-doc sgml-base-doc perlsgml w3-recs opensp libxml2-utils systemd-container systemd-homed
systemd-userdbd systemd-boot libip4tc2 libqrencode4 libtss2-esys-3.0.2-0 libtss2-mu-4.0.1-0
libtss2-rc0 libtss2-tcti-device0 polkitd accountsservice evince xdg-desktop-portal-gnome
debhelper
The following NEW packages will be installed:
adwaita-icon-theme alsa-topology-conf alsa-ucm-conf aspell aspell-en at-spi2-common at-spi2-core
bsdextrautils bubblewrap dbus dbus-bin dbus-daemon dbus-session-bus-common
dbus-system-bus-common dbus-user-session dconf-gsettings-backend dconf-service
dictionaries-common dmsetup docbook-xml emacsen-common enchant-2 fontconfig fontconfig-config
fonts-dejavu-core fonts-dejavu-mono fuse3 gir1.2-girepository-2.0 gir1.2-glib-2.0
glib-networking glib-networking-common glib-networking-services groff-base
gsettings-desktop-schemas gstreamer1.0-gl gstreamer1.0-plugins-base gstreamer1.0-plugins-good
gstreamer1.0-x gtk-update-icon-cache hicolor-icon-theme humanity-icon-theme hunspell-en-us
iso-codes libaa1 libargon2-1 libasound2-data libasound2t64 libaspell15 libasyncns0
libatk-bridge2.0-0t64 libatk1.0-0t64 libatomic1 libatspi2.0-0t64 libavahi-client3
libavahi-common-data libavahi-common3 libavc1394-0 libcaca0 libcairo-gobject2 libcairo2
libcap2-bin libcdparanoia0 libcolord2 libcryptsetup12 libcups2t64 libdatrie1 libdbus-1-3
libdconf1 libdeflate0 libdevmapper1.02.1 libdrm-amdgpu1 libdrm-common libdrm-intel1 libdrm2
libduktape207 libdv4t64 libdw1t64 libegl-mesa0 libegl1 libelf1t64 libenchant-2-2 libepoxy0
libevdev2 libfdisk1 libflac12t64 libfontconfig1 libfreetype6 libfribidi0 libfuse3-3 libgbm1
libgdk-pixbuf-2.0-0 libgdk-pixbuf2.0-bin libgdk-pixbuf2.0-common libgirepository-1.0-1 libgl1
libgl1-mesa-dri libgles2 libglib2.0-0t64 libglib2.0-data libglvnd0 libglx-mesa0 libglx0 libgpm2
libgraphene-1.0-0 libgraphite2-3 libgstreamer-gl1.0-0 libgstreamer-plugins-base1.0-0
libgstreamer-plugins-good1.0-0 libgstreamer1.0-0 libgtk-3-0t64 libgtk-3-bin libgtk-3-common
libgudev-1.0-0 libhandy-1-0 libharfbuzz-icu0 libharfbuzz0b libhunspell-1.7-0 libhyphen0 libicu74
libiec61883-0 libjavascriptcoregtk-4.1-0 libjbig0 libjpeg-turbo8 libjpeg8 libjson-c5
libjson-glib-1.0-0 libjson-glib-1.0-common libkmod2 liblcms2-2 liblerc4 libllvm20
libmanette-0.2-0 libmate-desktop-2-17t64 libmp3lame0 libmpg123-0t64 libncurses6 libnss-systemd
libogg0 libopus0 liborc-0.4-0t64 libpam-cap libpam-systemd libpango-1.0-0 libpangocairo-1.0-0
libpangoft2-1.0-0 libpciaccess0 libpipeline1 libpipewire-0.3-0t64 libpipewire-0.3-common
libpixman-1-0 libpng16-16t64 libproxy1v5 libpulse0 libpython3-stdlib libpython3.12-minimal
libpython3.12-stdlib libraw1394-11 libreadline8t64 librsvg2-2 librsvg2-common libsecret-1-0
libsecret-common libsensors-config libsensors5 libsharpyuv0 libshout3 libslang2 libsndfile1
libsoup-3.0-0 libsoup-3.0-common libspa-0.2-modules libspeex1 libsqlite3-0
libstartup-notification0 libsystemd-shared libtag1v5 libtag1v5-vanilla libtext-iconv-perl
libthai-data libthai0 libtheora0 libtiff6 libtwolame0 libuchardet0 libunwind8 libv4l-0t64
libv4lconvert0t64 libvisual-0.4-0 libvorbis0a libvorbisenc2 libvpx9 libvulkan1 libwavpack1
libwayland-client0 libwayland-cursor0 libwayland-egl1 libwayland-server0 libwebkit2gtk-4.1-0
libwebp7 libwebpdemux2 libwebpmux3 libwebrtc-audio-processing1 libwoff1 libx11-xcb1
libxcb-dri3-0 libxcb-glx0 libxcb-present0 libxcb-randr0 libxcb-render0 libxcb-shm0 libxcb-sync1
libxcb-util1 libxcb-xfixes0 libxcomposite1 libxcursor1 libxdamage1 libxfixes3 libxi6
libxinerama1 libxkbcommon0 libxml2 libxrandr2 libxrender1 libxshmfence1 libxslt1.1 libxtst6
libxv1 libxxf86vm1 libyelp0 lsb-release man-db mate-desktop mate-desktop-common mate-user-guide
media-types mesa-libgallium mesa-vulkan-drivers networkd-dispatcher python3 python3-dbus
python3-distro python3-gi python3-minimal python3.12 python3.12-minimal readline-common
session-migration sgml-base sgml-data shared-mime-info systemd systemd-dev systemd-resolved
systemd-sysv systemd-timesyncd tzdata ubuntu-mono x11-common xdg-dbus-proxy xdg-desktop-portal
xdg-desktop-portal-gtk xdg-user-dirs xkb-data xml-core yelp yelp-xsl
0 upgraded, 266 newly installed, 0 to remove and 0 not upgraded.
Need to get 169 MB of archives.
After this operation, 781 MB of additional disk space will be used.
With no install recommends (+172 MB)
[user@ff9d9355db73 ~]$ sudo apt install --no-install-recommends mate-desktop
[sudo] password for user:
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
The following additional packages will be installed:
adwaita-icon-theme at-spi2-common dbus dbus-bin dbus-daemon dbus-session-bus-common
dbus-system-bus-common dbus-user-session dconf-gsettings-backend dconf-service fontconfig
fontconfig-config fonts-dejavu-core fonts-dejavu-mono gtk-update-icon-cache hicolor-icon-theme
humanity-icon-theme iso-codes libargon2-1 libatk-bridge2.0-0t64 libatk1.0-0t64 libatspi2.0-0t64
libavahi-client3 libavahi-common-data libavahi-common3 libcairo-gobject2 libcairo2 libcolord2
libcryptsetup12 libcups2t64 libdatrie1 libdbus-1-3 libdconf1 libdeflate0 libdevmapper1.02.1
libepoxy0 libfdisk1 libfontconfig1 libfreetype6 libfribidi0 libgdk-pixbuf-2.0-0
libgdk-pixbuf2.0-common libglib2.0-0t64 libgraphite2-3 libgtk-3-0t64 libgtk-3-common
libharfbuzz0b libicu74 libjbig0 libjpeg-turbo8 libjpeg8 libjson-c5 libkmod2 liblcms2-2 liblerc4
libmate-desktop-2-17t64 libpam-systemd libpango-1.0-0 libpangocairo-1.0-0 libpangoft2-1.0-0
libpixman-1-0 libpng16-16t64 libsharpyuv0 libstartup-notification0 libsystemd-shared
libthai-data libthai0 libtiff6 libwayland-client0 libwayland-cursor0 libwayland-egl1 libwebp7
libx11-xcb1 libxcb-render0 libxcb-shm0 libxcb-util1 libxcomposite1 libxcursor1 libxdamage1
libxfixes3 libxi6 libxinerama1 libxkbcommon0 libxml2 libxrandr2 libxrender1 mate-desktop-common
shared-mime-info systemd systemd-dev systemd-sysv ubuntu-mono xkb-data
Suggested packages:
isoquery colord cups-common low-memory-monitor gvfs liblcms2-utils mate-desktop-environment
systemd-container systemd-homed systemd-userdbd systemd-boot libip4tc2 libqrencode4
libtss2-esys-3.0.2-0 libtss2-mu-4.0.1-0 libtss2-rc0 libtss2-tcti-device0 polkitd
Recommended packages:
librsvg2-common at-spi2-core dmsetup libgdk-pixbuf2.0-bin libglib2.0-data xdg-user-dirs
libgtk-3-bin mate-user-guide networkd-dispatcher systemd-timesyncd | time-daemon
systemd-resolved libnss-systemd
The following NEW packages will be installed:
adwaita-icon-theme at-spi2-common dbus dbus-bin dbus-daemon dbus-session-bus-common
dbus-system-bus-common dbus-user-session dconf-gsettings-backend dconf-service fontconfig
fontconfig-config fonts-dejavu-core fonts-dejavu-mono gtk-update-icon-cache hicolor-icon-theme
humanity-icon-theme iso-codes libargon2-1 libatk-bridge2.0-0t64 libatk1.0-0t64 libatspi2.0-0t64
libavahi-client3 libavahi-common-data libavahi-common3 libcairo-gobject2 libcairo2 libcolord2
libcryptsetup12 libcups2t64 libdatrie1 libdbus-1-3 libdconf1 libdeflate0 libdevmapper1.02.1
libepoxy0 libfdisk1 libfontconfig1 libfreetype6 libfribidi0 libgdk-pixbuf-2.0-0
libgdk-pixbuf2.0-common libglib2.0-0t64 libgraphite2-3 libgtk-3-0t64 libgtk-3-common
libharfbuzz0b libicu74 libjbig0 libjpeg-turbo8 libjpeg8 libjson-c5 libkmod2 liblcms2-2 liblerc4
libmate-desktop-2-17t64 libpam-systemd libpango-1.0-0 libpangocairo-1.0-0 libpangoft2-1.0-0
libpixman-1-0 libpng16-16t64 libsharpyuv0 libstartup-notification0 libsystemd-shared
libthai-data libthai0 libtiff6 libwayland-client0 libwayland-cursor0 libwayland-egl1 libwebp7
libx11-xcb1 libxcb-render0 libxcb-shm0 libxcb-util1 libxcomposite1 libxcursor1 libxdamage1
libxfixes3 libxi6 libxinerama1 libxkbcommon0 libxml2 libxrandr2 libxrender1 mate-desktop
mate-desktop-common shared-mime-info systemd systemd-dev systemd-sysv ubuntu-mono xkb-data
0 upgraded, 94 newly installed, 0 to remove and 0 not upgraded.
Need to get 38.8 MB of archives.
After this operation, 172 MB of additional disk space will be used.