MT has no story and none of the characters ending to the games are canon. Midway Arcade Treasures 2 for the Nintendo GameCube, PlayStation 2, and Xbox has both normal versions of MKII and III. Midway Arcade Treasures Deluxe Edition for the PC has all three games.
So far, MK4/MK Gold has not been ported over outside the PS1/N64/Dreamcast/PC. Maybe WB will release it on Xboxlive and PSN.