If money is no problem, there's a vast library of excellent (and shockingly expensive) STG/shmup/maniac shooters to explore. Personally I invested in a modded Saturn in order to be able to play backups and not have to shell out $600 for something like Hyper Duel. Here's a link that covers most of them:
http://www.racketboy.com/retro/sega/saturn/sega-saturn-shmups-2d-shootersI also think the collection of Sega's Super Scaler arcade games is mostly superb. Out Run, Space Harrier, After Burner, Power Drift, and Galaxy Force II are all very close to arcade perfect, and they all benefit from either the Racing Wheel or the Mission Stick. The one exception in this series is Gale Racer, which is a very poor port and just not worth playing, I'm sad to say.
Other fighting games that you might look into - Fighting Vipers and the VF/FV crossover, Fighters Megamix. Last Bronx has a really elaborately designed world and backstories for its characters. Virtua Fighter Kids is funny and it's crazy that there was a time when such a silly idea for a game could be a full retail release.
Of course, the Panzer Dragoon games are masterpieces, all three of them.
Among 3D racing games, you're definitely going to need a racing wheel. Manx TT is an excellent game. Sega Rally and Daytona are great, of course. Virtua Racing and Race Drivin' are cool because they are so faithful to the arcade games, while adding in additional courses and cars, but they certainly aren't pushing the system's limits. There are also a number of interesting and somewhat lesser-known drifting games, like Touge King the Spirits.
