I wouldn't give my mother a used computer. I would try my best to get her a new one. Hell, the way smartphones and tablets are out selling desktops these days, you can find desktops for bargain prices. But if you can't get a new PC, I suggest PClinuxOS
with the KDE Desktop, LXDE Desktop, or XFCE Desktop
Second, your mother will be lost with ubuntu with the unity desktop, lens, HUD and etc. PClinuxOS KDE is as close to a windows look as it can get.
lastly, PClinuxOS has a FREE monthly magazine to get the most of there linux desktop. Of course, you do not need to be a PClinuxOS user to benefit from the HowTos/articles in there magazines.