The 32-bit era was known for two classic genres, the 2D fighter and the 2D shooter. In fact, most of the people that pick up my Saturn modchips are heavlily interested in building their shooter collection.
If you are interested in figuring out what the best shooters to start out or round out your game shelf, Shmups.com has an excellent thread for shooter fans that have both a Saturn and a PSX (or emulators). (I know, the thread is fairly old) It lists the shooters that are exclusive to each system and compares the games that both systems share.
(this is a repost for some of my newer readers)