You're now a cool person, congratulations! I've been a cool person since September 2000. xD
Let's see... I have 13 games for the Dreamcast:
Resident Evil: CODE Veronica, Skies of Arcadia, Grandia II, Dead or Alive 2, Shenmue, Jet Set Radio, Sonic Adventure, Space Channel 5, Rippin' Riders (Snow Surfers here in Europe, a passable snowboarding game), Soul Calibur, Metropolis Street Racer, Headhunter and Phantasy Star Online.
Of these I recommend you buy:
Resident Evil: CODE Veronica --- my favourite Resident Evil of all time;
Skies of Arcadia --- it's such an incredible JRPG, indeed at the level of past Final Fantasies. My only complaint is that it takes too long to get into and out of a battle, due to loading. I'm an impatient guy, so this grinds on me. But it is a great experience;
Grandia II --- the plot, the voice acting and the characters aren't as good as in Skies of Arcadia, but the battle system is pure bliss.
Shenmue --- An experience in itself. Unique and fondly remembered.
Jet Set Radio --- one of the epitomes of SEGA's creativity. I miss those days...
Space Channel 5 --- quirky, silly and crazy! And fun.
Metropolis Street Racer --- just an incredible racing game, I always prefered it over Gran Turismo and I am a Sony fan as well.
Soul Calibur --- the first and the best.
At the time, I also loved Sonic Adventure, Dead or Alive 2 and Phantasy Star Online, but the first is a bit annoying to me nowadays, the second has sequels and the third is half a game without the online. Rippin' Riders and Headhunter I care less about.