Advance Wars, Pokemon and Mario Kart I would recommend straight off the bat. The latter two have online functions, and the first one is just ace by itself.
As for the "attorney game", that would be the Pheonix Wright series. They're basically point-and-click adventure games, so if you like that kind of thing, you should enjoy it. The first two (Ace Attorney and Justice For All) are available on the DS (after originally being GBA games), and a fourth, full DS-implementing version is due out soon. I loved them both until Pokecrack took over my DS.
Hotel Dusk is apparently really good too, and is similar to Pheonix Wright, only with more adventuring/puzzle solving. It's fairly similat to Trace Memory I'm told, and I really liked that, so it's one I'd love to check out.