The correct answer is: pick any you like and see if it works well enough.
The one thing that would most likely cause problems and sluggishness is the graphics chipset. It is listed as working on https://help.ubuntu.com/community/RadeonDriver but I had a M200/X1100 myself and from 14.04 it became simply too sluggish. So you need to try and decide for yourself.
If the graphics chipset holds up, you can most likely run a full blown Ubuntu 16.04 with Unity, in 64-bit mode.
If that's too sluggish to your liking, try in order Lubuntu and then XUbuntu. After that, you most likely have to divert to other distros that are targeted to slower computers.
Good luck.