Whoah! There's a ton of great answers in here. Thank you all very much!
@KAI: Thanks for the input on L&D. ACE sounds exactly like the kind of thing I'm into [ROBOTS ROBOTS ROBOTS]. I had no idea there was a Melty Blood game for the PS2 either. Sweet. Psychic Force looks awesome too -- the concept of a flying fighting game is wholly radical. A lot of these other ones look great too, I wrote them down and I'm going through them one by one on youtube. Thanks!
I do have to say I'm a bit disappointed by "Kinnikuman Muscle Grand Prix 2 Tokumori" though. It doesn't look bad, but for a second I thought that
http://www.youtube.com/watch?v=nk2wViKSh_M might have been a real thing, and you sent my hopes crashing through the roof
@pestro87: Chain Dive looks fucking awesome. I looked up a couple more videos; I absolutely LOVE games with free or unusual flying, and this one looks extremely stylish and slick to boot. Thanks!
@NTSC-J (and by extent KAI): Games that also had a release in the EU are absolutely fine, since I only otherwise have an NTSC-U PS2, and they wouldn't work on my TV anyway. Gekisha Boy 2 looks incredibly silly, and like it'd be a lot of fun. Thanks!
As for the 'The Chikyuu Boueigun' games, I did know of them already, yeah, but I really want to know if they'd actually work on my system. I'll try and use the japanese titles when referring to games that had releases outside of Japan from now on. TCB2 especially looks amazing, as there's a character with a /jetpack/. I fucking love jetpacks.
@Kiken: Oh man, I had no idea the Sega Classic Collections had the option for english! Do you happen to know if Phantasy Star and Dragon Force do? That would be AMAZING. That was actually the only reason I haven't purchased the Monster World Collection yet already, so thank you very much for clearing that up!! Unfortunately, yeah, not too into Mahjong
@MOSQUITO FIGHTER: I had no idea what Galaxy Force was until just now. This looks fantastic, I love rail shooters. I also wasn't aware of how different the Taito Memories collections were from the American counterparts. I wasn't planning on getting them before, but now I'll have to seriously consider it. Especially for PuLiRuLa and the shmups (also tate support!). As for emulating them, I know you
can, but why would you want to?
@Jonathan Ingram: *whistles*, what a list. The Hanjuku Eiyuu games look like a blast, how easy are the mechanics to understand without Japanese, though? Hungry Ghosts and Shadow Tower Abyss were actually two of the main non-shmup games I was interested in for the console, so it gives a bit of extra validity to the rest of your list

. As for Busin 0 and Venus & Braves, same question as with Hanjuku Eiyuu. They look very fun, but the dialogue might be important... As for mojib-ribbon, does playing it make more sense than watching videos? Because I really can't tell what's going on there. Vib-Ribbon rocks, though. Boku no Natsuyasumi looks cute and fun; it reminds me of Chu♥lip. Kamizawa looks cool too, interesting take on the stealth mechanic. As for FFXII, is there any reason to not just get the NTSC-U version, and does this one have english subtitles?
Thank you all for your help! And while I'm here, I might as well point out this game I just found on HG101, which looks pretty damn cool:
http://hardcoregaming101.net/gunbike/gunbike.htm

Transforming robot bikes and 3rd person mech shooting. Life is great.
The one statement in bold above is so it stands out from the rest of this wall of text - I'd really like an answer on this.