Congrats Jon. I think you'll really enjoy it, as it sounds like a system that would be right up your alley. Lots of arcade style games. You may already know this, but the Dreamcast was essentially the home version of Sega's Naomi arcade board so lots of Dreamcast games are basically arcade perfect.
The Dreamcast has, in my opinion, the greatest 2d fighting library of all time. Street Fighter 3/Double Impact/Third Strike, Street Fighter Alpha 3, Marvel vs Capcom, Marvel vs Capcom 2, Super Street Fighter IIX (best version of SF2), Capcom vs SNK, Capcom vs SNK 2, Vampire Chronicles (basically a Street Fighter Aplha 3 version of Darkstalkers), Last Blade 2, Garou: Mark of the Wolves (best SNK fighting game ever!), Jo Jos Bizzare Adventure, the list goes on and on.
Listen to the others here about burning games onto CD-Rs. Piracy was pretty rampant on the Dreamcast because you didn't have to mod a thing to play pirated games. I'm against piracy when a system is alive and well, but am I really gonna put $150 in a price-gouging reseller's pockets for Cannon Spike (awesome 3D Capcom arcade game)? Nope. So I burned it and play it for free.
The system has awesome sports games, which I don't usually like, but Virtua Tennis and the Tony Hawk games have aged very well. Look into Sega's other 2K games, too.
Buy a VGA cord off Amazon for $20, find someone giving away a CRT computer monitor on Craig's list, get a decent surround sound system and enjoy how ahead of their time Sega was with the Dreamcast. I have one CRT monitor in my game room and 3 back-ups in my garage. They're nice monitors and all 4 were free. I have a second Dreamcast hooked up to my Sony Wega Trinitron with S-Video, which is what I suggest if you don't wanna go the VGA route. Combined S-Video & RCA cables are also about $20 or less on Amazon and highly recommended if you don't get a VGA setup. Composite cables suck.
I know you hate RPGs, but the Dreamcast has two fantastic ones with Skies of Arcadia and Grandia II. Shenmue should be tried as well. Just in case you change your mind about an awesome gaming genre.
Enjoy your Dreamcast.