The others have already pretty much covered the mod-chip discussion, so I can’t add much except: it’s really not that big a deal. 99.99% of the time, if a Japanese title is cool enough, it will get ported to a US version. (Vib Ribbon being a notable exception… grrrrr…)
IMO, the only reason to have a can-play-imports mod chip is if there’s some obscure Japanese-only title you have to have, or if something really big just came out and you can’t wait for the companies to get around to translating it. I work in videogames, and I just recently got a mod-chip, and then only because I really, really wanted a Taiko drumming game I bought in Tokyo. For somebody who’s a self-confessed casual gamer, I don’t really see the point of going through the hassle and extra expense.
My recommendations:
Baldur’s Gate: Dark Alliance is as close to a console version of Diablo as I’ve ever seen. (It’s not much like the PC Baldur’s Gate at all). Very streamlined RPG action gameplay, using a modified version of the 3rd Edition D&D rules, I believe. It’s a hell of a lot of fun. I haven’t tried the sequel, but it’s out there.
The Tony Hawk Pro Skater series is excellent all around (I haven’t tried Underground). I never, ever would’ve imagined I’d like a skateboarding game, but it’s just plain fun, even to people who couldn’t care less about skateboarding.
Same with SSX Tricky and SSX 3, but with snowboarding. I don’t think they’re as much fun as the Tony Hawk games, but they’re flashier.
In the rent-it-first category:
Rez is pretty cool, but I wish I’d rented it first. Not much long-term value to it, and it’s not really a “game” so much as an interactive music demo. If you like it, Amplitude is another music game that’s kind of like it (but not as imaginative), and it uses licensed music.
ICO is one of the best games I’ve ever played for any platform, but it may not be your thing. You play as a boy who has to guide a girl out of a castle as you’re both pursued by strange shadow creatures. It’s very puzzle-oriented, but they’re all ingeniously designed and on backgrounds that are just stunning. I usually describe it as being like MYST, if MYST had been rendered in real time and you actually cared what was going on.
Gitaroo-Man has already been mentioned, but I’ve got to second it. It’s very weird, and there may not be a lot of replay value to it, but it’s just cool.
Devil May Cry is the stupidest game I’ve ever loved. It’s way, way over the top and feels like a cheesy Hong Kong action movie turned into a videogame. There’s just something indescribable about using your two big-ass pistols to juggle evil reanimated marionettes in the air, while the screen flashes the words “Bravo!” and “Stylish!” on the screen.
Onimusha and Onimusha 2 are basically Resident Evil set in feudal Japan. I like them better than the RE series because you use melee weapons (swords), which are much easier to manage with the RE control scheme. The soul-sucking bit is neat, too.
Prince of Persia: The Sands of Time is a very slick game, but you have to like jumping puzzles.
And if you change your mind and decide you do like story-driven games:
Final Fantasy Tactics is the best game ever made. (It’s a PS1 game, that will run on your PS2 if you get a PS1 memory card).
Suikoden III is a solid console RPG, but I’ve always loved the Suikoden series so I don’t know how non-console-RPG fans will take it. It’s not as spectacular as Final Fantasy X, but it also is more interactive and slightly less linear. I think the Suikoden games are all about fun, while the FF series is all about the spectacle and the story.
And I haven’t played them myself, but I’ve heard several people say that Ratchet and Clank and Ratchet and Clank 2 are the best platforming games around.