The first Bonk's Adventure is the best one. It's not that long, but it has Bonk's signature super-smooth spinning move that was taken out of the later games. Bonk's Revenge is pretty good other than the missing spin move (which takes a lot from the game mechanics IMO). Bonk III is just a clunky, unfun mess.
Shooters
Aero Blasters
Blazing Lazers
Galaga '90
Ordyne
R-Type
Raiden
Side Arms
Soldier Blade
Super Star Soldier
Action
Parasol Stars
Action RPG
Dungeon Explorer
Neutopia or Neutopia II (the first will be cheaper)
Dragon's Curse (side scrolling action/platformer with some RPG elements, same as Wonderboy III: Dragon's Trap on SMS, outstanding game)
Strategy
Military Madness
Side Scrolling Action
Cadash
The Legendary Axe (the second one was junk)
Ninja Spirit
Splatterhouse
Platformer
J.J. & Jeff (this is actually a decent Mario-style platformer)
Bonk's Adventure
New Adventure Island
Pinball
Alien Crush or Devil's Crush
Puzzle
Klax
Racing
Moto Roader
Sports
World Class Baseball (the later games only released in Japan are better, but this is a good solid baseball game)
TV Sports Hockey
I left out some of the really expensive games like Air Zonk or Magical Chase. They're good, but not worth the price you'd pay nowadays IMHO. If you want some import recommendations, let me know.
Did you get him a CD attachment as well? You mentioned the Thunder games, so I assume so. Some good domestic CDs:
Beyond Shadowgate - excellent adventure game
LOOM - another great adventure game, really beautiful graphics and soundtrack plus a very unique setting
Dungeon Explorer II - more Dungeon Explorer with nice cut scenes. This game will probably be VERY expensive if you can find it. Only grab if you find it cheap, it's definitely not worth the $100-plus I sometimes see if go for on eBay
Monster Lair - nice side-scrolling shooter
Dynastic Hero - in the same series as Monster Lair, but this is an action/platformer game. Rather rare though so might be pricey
Shape Shifter - good side scrolling action/platform type game
Vasteel - engrossing strategy title
Most of the above are Super CD games, so you'd need either a System Card 3.0 or a Duo to play them.