The device looks like it'll be good to play most games upto the PSP. While I can suggest the usual suspects, Super Metroid, Metroid 4, SotN, Pokemon I'm going to suggest odd-ball games which I like
Game Boy
Super Mario Bros Deluxe (NES Mario 1 & JP Mario 2 with saves and bonus features)
Harry Potter 1,2,&3 (Turn Based RPGs, bit rough but an excellent sound track)
Mickey's Speedway USA (made by Rare, fantastic soundtrack, top down racer, GBC game so controls are wonky)
GBA
Crash Nitro Kart (smoother and plays better IMHO than Super Circuit, controls require some patience to master)
Spongebob Squarepants the Movie the Game (Made by Wayforward, and is better than I'd expect a license game to be)
Jurassic Park Operation Genesis (Zoo tycoon with Dinos on GBA)
Genesis
Ren & Stimpy Stimpy's Invention (beautiful and painful platformer)
TMNT Hyperstone Heist (Turtles in Time, but legally distinct so Nintendo didn't sue)
Scooby-Doo Mystery (A point and click adventure on the Genesis, yes they made one)
I got a retroid pocket 3+ for Christmas. Loaded it up with JRPGs, but this list seems like some fun games to play when I finish one so I don't burn out on that genre. Thanks a lot!
I feel most games we have today are just reskins of open world/action rpg lol.
I am in the middle of a game session of Breath Of The Wild and I wanted something fresher and more action packed (and with a badass soundtrack) and I picked up almost blindly Nier Automata, it is kinda what I was looking but still open world and action RPG haha, my bad for not doing the proper research though.
I haven't played most of these, but I will gladly add an endorsement to the early Harry Potter games. They often only tangentially related to the movies, but they had some awesome mechanics, and played into the full story really well.
Cannot recommend Panzer Dragoon Saga enough. One of the best looking Sega Saturn games. Its a JRPG with turn-based battles, a super unique system. Along with the rest of the Panzer Dragoon series (though they are on-rails arcade shooters), not sure the RP3 is powerful enough for original Xbox games.
For driving, I am sure you've already been recommended the usual, but to reiterate: anything from Gran Turismo, Star Wars Episode 1 Racer, Collin McRae, WipeOut, Need for Speed, and Sega GT are all good picks.
For platformers, definitely try Yoshi's Island if you haven't already. If the visual style is a turn off, try to roll with it until at least the second boss. Great gameplay.
For a turn-based RPG, you'll frequently get Final Fantasy recommended but if you'd like to also try the other big series, give Dragon Quest V a shot. Otherwise I second the recommendations for Advance Wars (strategy) or Tactics Ogre (strategy JRPG, go with the PSP version for your hardware).
I've been going through the old Final Fantasies. I finished FF5 and FF6 last year and recommend both. They have great pacing (They change things up before it gets too stale) and if you keep an online guide handy, it's not as frustrating as it was when I was 10.
Not sure what they have available, but Advance Wars and Tactics Ogre I both had fun with. I heard good things about the Disgaea games (the fourth one in particular), too, but never played them.
IDK what games are actually compatible with your device, but I do have opinions about cool older games.
turn based:
Civilization
Master of Magic
Champions of Krynn, Death Knights of Krynn, and Dark Queen of Krynn
Shadowrun Returns, Shadowrun: Dragonfall, and Shadowrun: Hong Kong
Arcanum: Of Steamworks and Magic Obscura
Oh, I've never played that version. But handheld ports of games in olden days are usually on the shit-tier. Even if the achievement of porting it is commendable.
God Medicine on GameBoy is a massively underrated RPG. Best one on GB imo, and well worth anyone's time. You'll be constantly surprised they did so much with a GB game and the theme and story is relatively unique even to this day.
In addition to stunt car racer, Brøderbund’s Stunts is great. Also Big Red Racing is fun. Wacky Wheels is a good Mario kart clone. Good old school nascar games are fun if you like circle track driving.