I've got all of those DC titles on my XBox...well, I have some Guilty Gear on my Xbox (not Overture). Not a Twisted Metal fan. And I believe someone else mentioned Fear Effect and agreed to look into it.
Oh, and I don't know if this would interest you, but there's a thing called NesterDC which is basically an NES emulator with nearly every NES game out there built in that you can burn onto a CD and play using your Dreamcast. I've played that more than all my DC games combined.
For Dreamcast, you have to get Spiderman. It was an incredibly fun game (mine stopped working ) that is a must-have for that system. They have the same version for PS1 as well, but I'm biased towards the Dreamcast, since that's what I had. Soul Caliber for the same system was really good (that one stopped working too for me... I lost a few good games on that one.). I haven't played Jet Set Radio, but that looks pretty good too.
-Legacy of Kain: Soul Reaver is a pretty radical action adventure game. Definitely give that a go! -Soul Blade is a nice fighting game, if you like that sort of thing. Eventually became Soul Calibur, so it's interesting to see how it began. -Forsaken is a pretty sweet first person game that's HELLA FUN in multiplayer. Can't really think of anything to compare it to, but it's still pretty good by today's standards! -Roll Cage 2 is a VERY underrated racing game that really deserves more love than it got. Seriously, there's so much in this game that's so fun and enjoyable it's a damn shame it hasn't got a remake or another sequel.
Dreamcast: Typing of the Dead. You'll need a keyboard, but you can get keyboard plus game for PRETTY cheap, like $20. This is my favorite game of all time. Sadly it seems to my memory that a lot of the great Sega franchises never came out on this system. I can think of an exception, but it's an RPG.
PS1 had a lot of great fighters if you're into those. I think the last PS1 game I actually booted up was called Silhouette Mirage which is a ... 2D platformer/shooter by Treasure of all people. At any rate I would definitely track down all the Castlevanias that came out for it, there's one called Chronicles that's perfectly cromulent.
Oh, also Vagrant Story and Valkyrie Profile. Well, ok, I guess you could call Valkyrie Profile an RPG, but it's not in your typical RPG mold. Vagrant Story is a 3D action game.
It's weird to me that DC burnable ROMs are hard to come by these days, pirating was widespread back in the day and I personally think it helped kill the poor Dreamcast. Er, not that you should do that, the games are cheap enough without it.
DC: Definitely get Shenmue, and Shenmue 2(The DC version of Shenmue 2 wasn't released in NA, but since you modded it, get the EU version, the text is in english, so you'll have no problem playing)
PS1: (Are you kidding me, there are way too many games to list, but you can start with these) Make sure to get FF Anthology(it is the best FF compilation ever, it has the never before released outside of Japan FF 5, and a pretty much perfect port of FF6), get Dragon Warrior 7, Castlevania Symphony of the Night, Final Fantasy Tactics, Brigandine, Tactics Ogre.