Get a Saturn and get the following games except Liquid Kids, it's a fantastic game but is a little too high for it's own good, I just got lucky to find it for under $100.
Gradius Deluxe Pack
Parodius Deluxe Pack
Twinbee Deluxe Pack
Jikkyou Oshaberi Parodius
Sexy Parodius
Cleopatra Fortune (another expensive one, if not for the Taito Legends and Memories version, I'd have no version to play. Used to go for around $50, now much higher, so I don't own the Saturn version) - great puzzler
Puyo Puyo Tsuu
Puyo Puyo Sun
Metal Black
Bubble Symphony
Puzzle Bobble 2/Bust A Move 2
Puzzle Bobble 3
Game Tengoku (aka The Game Paradise, Jaleco cute em up, really really good)
Street Fighter Alpha 1-3
Saturn Bomberman (go for the Japanese version, US version is far too expensive for it's own good, even I still need this game)
Layer Section (great shmup, thank me later) - available in the US as Galactic Attack (silly rename)
Layer Section II
Darius Gaiden
Darius II (Saturn version has zoom in and out, my eyes burn as the sizes seem too big or too small for me)
Virtua Fighter 2
Elevator Action Returns
Outrun (best port of this game even today)
Daytona USA though it's not the best port of the game
Gun Frontier (cheaper on Taito Legends 2, one of the 4 Arcade Gears titles, this one didn't see PS1 release though)
Pulirula (again an Arcade Gears title, kinda pricy these days, mine was under $50 at the time)
Capcom Generation 2 (all the Makaimura games aka GnG you can handle)
Capcom Generation 4 (Mercs, Commando, Gun Smoke) CG 1, 2, 3, and 4 did see a release on Capcom Classics Collection PS2, but there's filters that the Saturn version does not have, clearer graphics go to Saturn. Street Fighter II insert revision here rounds out CG 5)
Capcom Generation 1 - 1942, 1943, 1943 Kai, old school Capcom shmups
Gekirindan - better port on Taito Legends 2, Saturn version is still nice, but pricy, recently passed up a copy while on vacation
Wonder 3 (another of the Arcade Gears, it too is pricy, but can be found cheaper on the second PS2 Capcom compilation, though it too has filters applied, another I passed on recently)
Image Fight/X-Multiply - this one is another Arcade Gears game, if you find it for $50, snag the damned thing as it goes for far higher on ebay, the most expensive of the AG titles. Passed on it awhile back on vacation, have a second shot that this time I didn't miss on, $57. Both shmups from Irem, Xing did the ports.
Hyper Duel (this one will kill your wallet, avoid unless you like spending money, though the game is from Technosoft, try in MAME first to suit your taste. The game may even grow on you quickly.)
Battle Garegga, great Raizing shmup, but far too costly
Batsugun - Toaplan's last official game as a company, see Battle Garegga for price.
Kingdom Grandprix found this one for a mere $20, great Raizing shmup/racer, isn't always cheap though
Gunbird - Psyikyo shmup, kinda bullet hellish, not bad at all.
Sonic 3D Blast - kicks the shit out of the Genesis version, not as bad as people say.
I'll stop here for suggestions though, explore the rest of the library on your own.
edit: I believe Keio Geketai is the sequel to Keio Flying Squadron on the Sega CD. There is also a prequel to Beyond Oasis also on the Saturn, as well as the third Shining Force, but only 1 episode got released in the US, the final two are Japan only and untranslated.