I remember the Dreamcast...plan on getting one myself too before too long. Anyway, you wanna know what games you need so...
BIG-BLANKET STATEMENT: Capcom Fighters. Street Fighter Alpha 3, Marvel vs Capcom 2, Power Stone...Capcom basically dominated the Dreamcast with its fighting games. You can't really go wrong with any of them.
Crazy Taxi
Gauntlet Legend
Jet Set Radio
Resident Evil: Code Veronica
Skies of Arcadia
Spawn: In the Demon's Hand
Sonic Adventure
Sonic Adventure 2
Soul Caliber
Typing of the Dead (or just House of the Dead 2 if you can't find a keyboard)
I know there are more but that should keep you occupied. Seriously though, Capcom Fighters. All of them. Ever (on the Dreamcast). I don't know if it's Capcom or not but Jojo's Bizarre Adventure is also worth mentioning. That and Sword of the Berserk but only if you're a fan of those anime series respectively.