I do suggest picking up the Ys and Valis series for the Turbo Duo as they're really really good games!
You may also want to try out Sapphire and Cotton!
If you're new to the Turbo Duo, try Valis III before the rest of the games. Although there a lot of us who love the series, the games aren't without their faults and aren't universally appealing.
You can't play Sapphire unless you either drop $75 - $150 on a converter or $150 on a PC Engine Duo system + $20 - $30 on an Arcade Card Duo + $200 - $400 on the game itself. So even if you just download and burn Sapphire or buy one of the bootlegs for $60, you'll still have to spend a bunch of money before you can play it.
You should try the arcade version of Cotton on Mame before buying the Turbo or PCE versions. Its another game that some people love, but isn't so hot gameplay or graphics wise by Turbo standards.
Here are some good cheap games to look into first, all of which will work on your system as-is-
CD:
Lords Of Thunder
Monster Lair
Forgotten Worlds
Dragon Slayer
Exile
Dungeon Explorer II PCE*
Kaze No Densetsu/Legend Of Xanadu II PCE*
Dynastic Hero PCE*
Neo Nectaris***
Vasteel***
Side Arms Special
HuCard:
Aeroblasters
Ninja Spirit
Bloody Wolf
Dungeon Explorer
Dragon's Curse
Blazing Lazers
Dead Moon
Legendary Axe**
Alien Crush
Cadash
Bomberman '93
Neutopia
Military Madness***
Samurai Ghost
Side Arms
*little on no japanese knowledge required.
**people seem to either love it or hate it.
***technically war sims, but people who hate war sims love 'em.