PS2 is my personal favorite system, but for kids IMO the Gamecube is probably the best choice.
Since there are three of them, you can get Mario Party and three controllers and all three of them can play. PS2 offers some multi-player games, but Gamecube beats the PS2 in that department. Just about all its good games are multiplayer.
Supersmash Brothers, just about any Mario game (mario baseball, mario party, mario tennis). Kids will fight for the controller. I know when I was a kid, id fight for the nintendo controller LOL