I as also just looking to purchase a Dreamcast, I had one long ago with crazy taxi. I saw one on craigslist for 200.00 with like 40+ games and a crap load of accessories. Wheel, controlers, those memory cards, and most of it looked brand new.

Shenmue I / II is a musthave
Virtua Tennis is really fun
Resident Evil Code Veronica was great too.

Ikaruga

Under Defeat

...and many more shmups!

Buy D2 if you can find it. Its one of my best games. I wish i can find a copy of it.

I bought a DC a few months ago too, haven't used it that much, but still nice to have. Shenmue is a must.

all the must have games that were on Dreamcast are on current or last en consoles.. id just by those games for an up to date system lol.

Grandia 2 is a good traditional RPG.

Cannon Spike - awesome capcom game with Cammy from Street Fighter
Typing of the Dead - House of the Dead using keyboards to type words to kill zombies. Very addicting.

That pretty much covers it.....

Crazy taxi 2 is still exclusive to Dreamcast so have a look for that......

Metropolis street racer is a fine racing game (great music too)

Powerstone 1 & 2 are great fun aswell

Dreamcast............ aaah, the memories

The system was great for the time ,although some of the genres werent all that well in number of games of quality released.

I have some 200+ Dreamcast games ,100 of wich were original ....later on I downloaded some japan-only games and games that didnt receive the gold status as Half Life 2 etc.

I would recommend you :

JRPG

Skies of Arcadia
Grandia II

FPS

Maken X
Half Life Blue Shift
Unreal II

Arcade

Crazy Taxi I and II
Cannon Spike
Spawn (Capcom game ,quite good)
Power Stone 1 and 2
Outrigger
Jet Set Radio

Sports

Virtua Tennis 1 and 2
Track and Field
NBA 2K
NHL 2K

Shot them up

Ikaruga

Racing

Ferrari F355
Metropolis Street Racer (the antecesor of Project Gotham )
Le Mans 24 hours
Sega Rally 2
Daytona USA

Fighting

Soul Calibur
Dead or Alive II
Project Justice

Adventure

Shenmue I
Shenmue II
Resident Evil Code Veronica
Headhunter
Resident Evil 2 and 3(if you havent played those ,you will be able to find it very cheap and these versions control quite well have less loading times etc)

Plattforms

Sonic Adventure
Sonic Adventure II

2D Fighting

Marvel vs Capcom 2
Streetfighter III:Third Strike (very important ,this is the best streetfighter game to date ,but dont buy the previous SFIII games ,dubbed Double Impact and something else)
Capcom Vs SNK 2:Fight of the Millenium
Streetfighter Alpha 3

Music-arcade

Rez
Space Channel 5
Space Channel 5 2
Samba de Amigo
Dance Dance Revolution

Gun games

House of the Dead 2
Confidential Mission
Virtua Cop 2