The only major differences in the Wii version of MK:A are that Khameleon is included in place of one of the Kreate-A-Kharacter slots, the controls are different (with Wii remote), there's an endurance mode, some control training, apparently some menus are a little different, and there is no online.
Your mileage may vary greatly. If you're really dying to play Endurance mode, or use Khameleon, knock your socks off...
Since the Wii is backwards compatible with GameCube games, you might want to get Deadly Alliance (and Deception), if you haven't done so already.

As for downloadable games, so far, there is nothing MK on the Wii. Only the PS3, 360, and PC got Mortal Kombat: Arcade Kollection. There doesn't look to be a good chance of it ever releasing on the Wii, unfortunately, as the Wii is much more of a family/kid console (in terms of most games - not including stuff like No More Heroes, and whatnot.)

For what it's worth, Midway Arcade Treasures was released on GameCube and would also be compatible on the Wii. So there is a way to play Mortal Kombat II and Mortal Kombat 3, though it's not perfect.