Since you are going for "action" and only played a few... you might as well go for some PS1/Saturn/N64 games to start with. Then work your way up to Dreamcast, Gamecube, Xbox and especially the PS2 (seriously, it has soooo many good games due to its preferred game developer use and long life).
I would start with some earlier games like Starfox 64, Pilotwings 64, Zelda: Ocarina of Time (if you don't mind longer adventure gameplay), Sin and Punishment, Megaman Legends (also on N64 as Megaman 64), Metal Gear Solid, Tenchu 1 and 2, Dino Crisis 2, Resident Evil 2, Tomb Raider 2, Ace Combat 2 and 3, Twisted Metal series, Syphon Filter series, Einhander, Ghost in The Shell, Dynamite Deka, Burning Rangers, Nights, Virtual-On, and Thunder Force 5. Wow, it is hard to think of 3D titles for the Saturn compared to so many good 2D titles it has.