My mom was just given a used computer, and I'm having trouble resetting it

[caravel]

Vista must have been horribly slow on that, even from a clean install and any newer version of windows won't be much better.

It will be a suitable system for a GNU/Linux system, but before you go down this route you should work out exactly what it is your mum needs to run on it. If it's just for web browsing then that's not a problem, but if there are some specific programs that would be required then you should research this before proceeding.

I would advise against gnome (and cinnamon which is a fork of gnome-shell) and KDE which are both on the heavy side.

The graphics should be ok, but don't waste time on the proprietary video driver as that GPU is unsupported. The FOSS driver (included in the Linux kernel) does support it.

I can't make any specific recommendation as I don't use or know much about the "easy" debian based distros (ubuntu, mint, etc). Just go with what others have said and give mint a try.

My preference would be for XFCE over Mate, but YMMV.

http://www.linuxmint.com/download.php