I highly recommend Ubuntu MATE for any use, however I'm not a big gamer but lot's of people run games on Ubuntu MATE.
A few things. The first PPA gezakovacs,.I looked and do not see that it has been updated for the 19.04 Disco release. What software were you looking to run via that PPA?
You can remove that PPA with this command sudo add-apt-repository --remove ppa:gezakovacs/name
substitute name with the name of the proper PPA
The Wine issue is two fold. The way to add Wine has changed and the PPA you used has been deprecated. Let's remove it by running: sudo add-apt-repository --remove ppa:ubuntu-wine/ppa
The commands are here to install Wine in 19.04: https://wiki.winehq.org/Ubuntu
If your system is 64 bit, enable 32 bit architecture (if you haven't already):
sudo dpkg --add-architecture i386
Download and add the repository key:
wget -nc https://dl.winehq.org/wine-builds/winehq.key
sudo apt-key add winehq.key
sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/ disco main'
sudo apt update
Then install the version you want : for example stable
sudo apt install --install-recommends winehq-stable