Umm... First off..
A US TurboDuo will allow you to play US HuCards, JPN CD 2.0 and most SCD (3.0) games. There is a faulty check mechanism in some demo disks and I believe Bonanza Brothers that will fail with a US SCD system (either US SCD Card or a US Duo). There is one game that uses the CD1.0 card, and that's Altered Beast CD. The game is playable, but you can't get past the 1st stage without a proper CD1.0 card.
To play JPN HuCards you'll need to get yourself a Converter (there are several, but the Kisado is so far the best one) or you need to mod your system. (From what I can tell, they've swapped a few pins.)
To play Arcade Card Games you need an Arcade Card DUO or Arcade Card Pro. Both of these are Japanese HuCards so you'll need a converter/mod in order to use them on a US System.
An Arcade Card Duo holds the extra Arcade Card Ram, and piggy banks unto the system's built in Super CD software. (So in the case of a (US) TurboDuo you'll still get the US Super CD boot-up screen even after you plug in a ArcadeCard Duo.)
An Arcade Card Pro hols the extra Arcade Card Ram and a Japanese Super CD software. This is the most universal card available as it will work with all cd-based systems (well, you need a converter/mod for US system). I usually recommend getting the ACPro (if you're getting an AC) because:
a) it doubles as an SCD card. If ever your Duo dies, you have the option of replacing it with a TurboGrafx-16 + CD attachement, PCENgine + CD Attachment, PCEngine Duo, TurboDuo. If you ever replace with a Non-Duo cd-based system, you'll have SCD and AC capability. If you go with an ACDuo, then you are much more limited.
b) It includes the Japanese SCD software which will enable you to use the one or two problem titles.
c) It's generally the same price (at one point they were cheaper.)
As for favorites...
There are loads of good games.
What genre do you want?
Umm... Off the top of my head (not including the ones you mentioned.)
Shooters:
Blazing Lazers (Hu), Soldier Blade (Hu), Magical Chase (Hu), Rayxander II (JCD2.0), L-Dis (JCD2.0), Spriggan (JCD2.0), Spriggan 2 (JSCD), Maccross 2036 (JSCD), Nexzr (or the Summer Carnival version called Nexzr Special) (JSCD), Sapphire (ACD), Parodius (JHu), Dentana Twinbee (JHu), Gradius II (JSCD), RType Complete (JSCD), Cotton (SCD)
RPGs:
Legend of Xanadu II (JSCD, boss fights are done like a brawler, you can have a 2nd player helping you.), Ys Book I&II (CD2.0), Ys Book IV (JSCD), AnEarth's Fantasy Story (JSCD), Cosmic Fantasy 2 (CD2.0, it's hard to start but after a while the story picks up.), Dragonslayer: Legend of Heroes (SCD)
Adventures:
Beyound Shadowgate (SCD), Loom (SCD), Dungeon Explorer (Hu, 5 player gauntlet), Dungeon Explorer II (SCD, 5 player gauntlet)
If you're into the Wonder boy games there are these ones:
-Wonderboy in Monsterland (JHu)
-The Dragon's Curse (Hu, same as SMS game Wonderboy III: The Dragon's Trap).
-MonsterLair (CD2.0): I believe this was the Arcade WonderBoy III. You had alternative shoot-em-up and wonder-boy like stages.
-Dynastic Hero (SCD): remake of Genesis' WonderBoy IV but heros are now bugs.
-(Closely related) New Adventure Island.
Umm...
Brawlers:
-SF2' Championship Edition (JHu)
-Art of Fighting (ACD)
-Fatal Fury 2/Special (ACD)
-Godzilla (SCD) (not amazing but decent for a Godzilla.)
Side Scrolling Brawlers:
-Ranma 1/2 Part 1 (JCD2.0, very good for a CD2.0)
-Riot Zone (SCD, not amazing, but okay'ish. This system doesn't have many side-scrolling brawlers)
-River City Ransom (JSCD, not too easy to find.)
-Umm...ahh... I don't remember the name of this game but I've got it.

I think it's "Warriors of Fate"? It's a capcom side-scrolling fighter. The player's fighter is always on horseback.
-Mad Stalker (ACD) Lots of recycled graphics, after initial load, everythign is there.
Digital Comics:
-Galaxy Fraulien Yuna (best one I've played) (JSCD)
-3x3 Eyes (JSCD/ACD)
Platformers:
-Yoshimoto Comedy (JSCD): themed backgrounds/characters, some weird Japanese Humour, mini-games.
-Shockman (Hu) (aka ShyubibinMan 2 (JHu)) and ShyubibinMan 3 (JCD2.0) are good Megaman-ish 2 player games. Alternating stages are shooters.
-Kaze Kiri (JSCD) a sort of Shinobi/Kenseiden like scroller
-Shadow of the Beast (SCD) this is probably *THE* definitive version of this game. It lacks some of the parallax scrolling in some areas (compared to the original Amiga version), the actual main character animation is better, controls work better with 2 buttons, the CD sountrack is top-notch as well.
Racing:
-Motoroader (and variants). The US only has "Motoroader". It's a 5 player top-down racing game.
-Victory Run isn't a bad Outrun clone, but it's not spectacular.
Sports:
-Davis Cup Tennis (JSCD, Hu). The game's the same be it on JSCD and Hu. I think you can pick it up cheap at NSCX (probably the only game they have left). It's okay.
Puzzle:
-Bomberman! (the original Bomberman comes hidden on the Gate of Thunder 4-in-1 disk making it a 5-in-1 disk.

), then there's Bomberman '93 and '94. If that's not enough, there's that Chicken Game that was released with one magazine that's a little similar.
-Buster Bros (CD2.0)
-Splash Lake (CD2.0)
Strategy:
-Military Madness (Hu)
-Neo Nectaris (JSCD aka Military Madness 2)
-Macross: Do You Remember Love (JSCD): fairly decent strategy game.
-Vasteel (CD2.0, you can play either side in the conflict, you can choose battles to be fought via computer control or you can control the duels. It's a strategy game based on different mechs. Each side has their own mech desings. I think there are about 20 different types of mechs as well.)
-Vasteel 2 (JSCD/ACD: It's compatible with the Mouse, the MemoryBase 128, uses up the Arcade Card if it's there. It's more a strategy game then the first Vasteel (which was more of a action/strategy)) This game plays a lot like the Macross strategy game, and at least count costs a lot less.
Umm... There are others. Not all of these are "must haves" but are titles that go into my mind.
You might want to look out for the Sherlock HOlmes titles if you want to see how PMV worked ont he Duo. (Umm, and then Gulliver Boy (JSCD) to see HuVideo FMV sequences.)
Other curiosities:
-Last Alert (CD2.0): The US version has TERRIBLE voice acting. The graphics aren't that great either, but it's a half-way decent Metal-Gear/Contra rip off.
-Final Zone II (CD2.0): About on par with Last Alert in voice acting. The graphics are better. It's a top-down commando-like game. I enjoy it.
