To answer this question simply- you need a PC-FX.
euh, theres 1 shmup on PC-FX.
and "great games" might not mean "cutesy dating sims that I can't even read"
anyway what you want ultimately is a US TurboGrafx16 and then a Duo-R
play US hucards on the TurboGrafx, play anything else on the duo-r
reason for this suggestion is, the cost it would take to region mod the duo-r is probably a bit more than you can grab a TG-16 for, and since you already have the TG-16 .....
just get you a duo-r for Japanese HuCards and for CD games (Since the Duo-R has save ram)
The best controller, in my honest opinion, is the Ave 3 or 6. They're both the same but have 3 and 6 buttons respectively. They are amazing. I love them.
As for games you just have to have, we will keep it Turbo Grafx-16 for now, until you get a duo-r, and then we will bombard you with more games....
Lifeforce (Salamander in Japan, I'm sure you have heard of it!)
Bloodywolf (It's the closest to Contra you're gonna get)
Keith Courage (Because everyone has to play the pack-in game)
China Warrior (Because I said so, and hope you become one of the fans of the old, giant sprite kung fu extravaganza)
Dungeon Explorer (It's Gauntlet, with content!)
Legendary Axe 1 and 2 (Very nice, eerie action platformers)
Bonk 1, 2 and 3 (The best platformer series ever)
Neutopia I and II (Zelda clones that are better than Zelda)
Parasol Stars (Bubble Bobble part 3! You hit stuff with an umbrella to very happy music, and it's beyond addictive)
Cadash (Best home version of the arcade game. It's kind of like Castlevania on dope, sort of)
Silent Debuggers (Hard to describe. First person cyberpunk action game. You'll either love it or hate it)
Military Madness (One of the greatest strategy games ever. Simple yet effective)
Fantasy Zone (Strange shoot em up game. Kind of obnoxious, totally colorful, addicting like crack)
I think that's a good list for now. Theres some more stuff too... most of these games can be had pretty damn cheap also.
Oh, and duh, Blazing Lazers. Its vertical shmup goodness.
As far as shmups go, you picked the right system.
and FINALLY,
go to pcengine.co.uk and you can quickly see some screenshots and gameplay videos of these games to see if they appeal to you.