EDIT: can anyone compile a short list of HU-CARD games for a beginner to the PC engine? I've jotted down a few thats been mentioned in past pages but i reckon there's little gems that no ones mentioned yet.
Thanks
Since you have a Japanese CoreGrafx I'll include the Japanese names in parentheses if different from the US title. These are based on my own opinion of "must have" cartridge games. Keep in mind US carts won't work on your Japanese system. I'm sure others will chime in with their own recommendations:
Air Zonk (PC Denjin)
Aero Blasters
Alien Crush
Devil's Crush (Devil Crash)
Batman
Dungeon Explorer **
The Legendary Axe
Legendary Axe II (Ankoko Densetsu)
Coryoon
Magical Chase
Wonderboy in Monster Land (Bikkuriman World) **
Wonderboy/Dragon's Curse (Adventure Island) **
Bomberman '94
Space Harrier
Gunhed
Final Soldier
Motoroader II
Ninja Spirit
Parasol Stars (Bubble Bobble III: Parasol Stars)
Parodius
Bonk series (PC Genjin 1 thru 3)
Salamander
Street Fighter II Champion Edition
Sinistron (Violent Soldier)
Splatterhouse
Also, these fall into the "would be nice" category:
Be Ball
Dead Moon
Samurai Ghost (Genpei Toumaden 2 / Kannoni)
Outrun
Paranoia
Terra Cresta II
** These games contain a more-than-average amount of in-game Japanese text. They should still be playable/winnable but you will not be able to enjoy the storyline unless you can read Japanese.
Also worth noting is that while Bomberman '94 is the best entry in the Bomberman series, Bomberman '93 has better music. '93 might be worth picking up down the road but if you have to choose one, go with '94. It has better gameplay and level design. The first Bomberman (Bomberman '92?

) should be avoided entirely unless it's given to you and/or you've played every other game available and you are really bored. The game drags on for 64 long tedious levels that are all very similar and you are treated to a killer soundtrack that consists of an entire 2 (TWO!!) whole songs that switch off each level.