Super Smash Bros. Melee is a very very good game. However, seeing that you haven't owned a (or at least said you have) Game Boy, NES, SNES or N64, SSBM won't fit as perfect as it does to Nintendo gamers. This game is a very VERY good nostalgia game, no doubt about it. I got it almost exactly a year ago (April 12, 2002) and even though it wore down after awhile, for some strange reason, I picked it up and it's almost like it's been completely revived, I go to tournaments, I practice everyday, I visit GAMEFAQS SSBM forums daily. This game is just so great. Other games...
-Sonic Mega Collection (Pretty nice collection of Sonic the Hedgehog games, you seem to have a lot of money to blow, don't miss this one out)
-Phantasy Star Online (GCN's best and only online game, great replay value)
-Super Mario Sunshine (Short but sweet, if you haven't played Mario 64, you're really in for a treat)
-Star Fox Adventures (I don't want to bash this game, it's not that bad. Good/Great music, awesome visuals)
-TIME SPLITTERS 2!!!!!!!! (From the makers of Goldeneye, need I say more. You problably have this game for XBOX)
-Skies of Arcadia Legends (Good RPG)
I always good forget games when I have to list them, DAMN IT!