I believe the version of linux you run would depend more on your hardware. . . if you have an old box, you dont want a new linux =probably wont meet the hardware requirements. .
As far as linux gui from windows, there are commercial Xwindows programs but. A no cost alternate is to install CygWin and use xwindows from that to access your linux box. . .
I.e (*$ xwin -:0 -query YourLinuxBoxName *)
As far as setting things up, start with the HOWTOs...
ask questions not answered there and someone should be able to help. . .