Not all games support 480p but those that do should work normally.
You have to see the "what games should I get" thread in its "historical" context though, the GC had a lack of games so many a game got overrated by the community and may not be worth buying nowadays.
There's the obvious candidates like Metroid and Zelda (including Four Swords Adventures), Viewtiful Joe (first one's better than the second) and of course the various Mario games (mostly the sports games and such but Paper Mario deserves a special mention) which will probably see superior sequels on the Wii but may be worth buying before then, too. Tales of Symphonia is a great game and worth getting if you see it.
Personal favourites include P.N.03, Gotcha Force and the Lost Kingdoms games but I wouldn't recommend buying these games sight unseen, they may not be your cup of tea. In my oppinion Skies of Arcadia and Ikaruga are overrated and not as good as other games in their genres, they stood out because the GC lacked in both.