Congrats on joining the cool kids club
The TG16 is best for shmups (especially the PC Engine imports), but as others have noted, it has a lot of fun, unique titles as well.
For me, the essentials:
Bonk's Adventure/Revenge: Get them in order, but they're both great. Funky platforming and bright colors, clever characters, and huge replay value (it's relatively short, not very difficult, and easy on the eyes).
Blazing Lazers: For me probably the best shooter on the system. Not nearly as hard as R-Type (which though has beautiful graphics), not nearly as expensive as Soldier Blade. Great chip sound.
Alien Crush: I'm one of those that prefer this pinball to Devil's Crush, though both are worthy. The music is great and the bonus screens I just feel are better. Time Cruise is quite good too but a totally different experience to the Crush games.
World Class Baseball: Dirt cheap and a quick play. Think RBI Baseball with much much much better graphics and a bit more sophisicated gameplay.
Bomberman '93: This is THEE multiplayer game, for any system. Get a TurboTap and 4 other controllers and find 4 friends/family members. Even my sister-in-law and mother-in-law will play this one if we fire it up. Much better than the original version and to me not as hokey as Bomberman '94 (PC Engine import only).
That's just a quick list. You should check out this site for great reviews/write-ups on both the US and Japanese games: www.thebrothersduomazov.com
It's not mine, but it's a friends and one of the more respected members of the TG/PCE community.