Linux Mint is a bit of a darling in the Linux world right now. Originally intended as an improvement on Ubuntu, Mint is slick and is a finalist in the “it just works” category for first-timers and more experienced folks.
It comes stock with the Cinnamon desktop but the MATE version is also downloadable and would probably be more useful to folks on older PCs. Note: if you do go Cinnamon try out the Cinnamon 2D option when you log in. Easier on the older hardware but has the same basic look.
Suitability for folks migrating from XP:
Install: 9. Uses the *buntu installer very nicely.
Grandma test: 8.5. Immediately useful for everything she would probably want to do.
Default applications: 10 Mint is known for the excellence of codec support (ie, her cat videos and music will all play fine right out of the box).
Speed: 8. Could be made faster by dropping in LXDE, Xfce or other lightweight desktop.
Updates: 8.5 Follows the Ubuntu release schedule.
Popularity: 9.9. Number 1 distro on DistroWatch. Huge numbers of interested users.