Hi can someone please tell the difference between the Ubuntu 16.04.3 LTS and the Ubuntu-MATE 16.04.01? And will the AMD64 image that downloads when i click the Ubuntu.com link work on my Pentium processor?
The amd64 designation is for 64-bit, either Intel or AMD cpu will work … you can try ubuntu (not install) to see if it works with your computer. There is a page that lists the min. requirements for Ubuntu Mate.
Ubuntu is a Linux distro based on Debian. It is offered by Canonical. Within 'buntu based systems, you can choose different desktop environments (a desktop environment is the bundle of programs that make the graphical environment you interact with, which runs on top of the actual OS). The plain Ubuntu offered by Canonical comes with the Unity DE, though they will be dumping that in favor of Gnome 3 next year.
Ubuntu-MATE is an official flavor of Ubuntu which comes with the Mate desktop environment. It's very nice (I'm using it right now!), and I chose it over Unity. I definitely recommend Ubuntu-MATE to new users. Basically, Ubuntu-MATE has the same core Ubuntu system, but a different graphic environment.
Regarding version numbers, both 16.04.1 and 16.04.3 are the Long Term Support (LTS) version. Ubuntu offers two main versions, a long term support release that is supported for 5 years but has older packages, and a short term release with a higher version number that is supported until the next release. Usually, you can tell the difference by "LTS" being in the name. You want 16.04.3, since it is the newest and most up to date version of the LTS. 16.04.1 isn't different, just older and out of date. If you see 16.04.1 available for download, don't use it. It's an outdated link.
I recommend the LTS, unless you are happy upgrading in a few months. It is your choice whether you want to try stock Ubuntu, Ubuntu-MATE, or another official flavor (you can find the total list of official flavors here). If you want Ubuntu-MATE, go to the official site and download it here.
I can't say without knowing the exact CPU you have, so I'll try to tell you how to find that out. 64 vs 32 bit refers to the size of the instruction set (32 vs 64 bits) that your CPU architecture can handle. If your computer is younger than ten years old, it is probably 64 bit.
To be sure, check the model number of your Pentium and google to find out it if it is 32 or 64 bit. If it is 64 bit, you want the AMD64 (sometimes also called X86_64, they are equivalent). If it is 32 bit, you want the X86 image. Hope that helps. 
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