RetroGaming

Earthbound on SNES is a timeless one. Advance Wars is an excellent turn-based series. I played it on GBA, but there are a bunch of versions.

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)

SNES

• Top Gear (It has a soundtrack that slaps)

PlayStation

• Pac-Man World 20th Anniversary (3D Platformer that's aged well)
• Scooby Doo and the Cyber Chase (A 3D Platformer that hasn't)
• Harry Potter 1&2 (We have the Legend of Zelda Ocarina of Time at home)
• Rugrats Search for Reptar (if you like the show you'll like the game, otherwise it makes PS1 Hagrid look like the monalisa)
• The Emperor's New Groove (3D Platformer that's aged a lot better than it should've)

PSP

• Star Wars Battlefront II, Renegade Squadron, & Elite Squadron (same concept, 3 different implementations, all have their pros and cons)
• Modnation Racers (yes they ported a PS3 game to a portable with less power than a PS2, and it's not half bad)
• LittleBigPlanet (same deal, just with a platformer)
• LEGO Star Wars II/LEGO Indiana Jones (PS2 games ported to PSP)

My RP3 is how I got completely absorbed into the trails series. Starting with Trails in the Sky and Trails in the Sky Second Chapter on PSP.

It's a top-scrolling shooter, but give Tyrian 2000 a go. It's free on GOG.

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.

Here's a mostly forgotten one: Phantom 2040 for SNES

Not truly a metroidvania, but an interesting platformer shooter with branching paths and many different endings.

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.

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

platformers:
Noita
Dead Cells

driving:
Gran Turismo 4

Chrono Trigger is really a must if you like JRPGs.

Obligatory Frog theme 🐸

As an MSDOS and platformer fan:

• Dangerous Dave (1990 version)
• Prince of Persia 1 & 2
• Crystal Caves
• Bio Menace
• Commander Keen series (keen 4 being the best)
• Jazz Jackrabbit series
• Jill of the Jungle
• Aladdin

My favorite from the above would be Bio Menace, followed by Dangerous Dave, Prince of Persia 1 and Jazz Jackrabbit.

Most of these games should be available on GOG, if not, search for "eXoDOS".

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.

Alley cat

Lost Vikings is a classic. Go for DOS or SNES.

Milon's secret castle. Top notch NES game.

Colin McRae Rally 1 & 2 for driving games.

How are you liking the RP3? I don't own a handheld myself but I'm always tempted to get one.

Rayman. The dos version will work, or the psx, jaguar or Saturn version. Whichever you prefer.

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.

Driving:

Stunt Car Racer (Amiga)

WipeOut 2097/XL (PSX)

Both are top-tier racing games.

Breath of Fire was a great turn-based RPG series that I don't think ever got enough recognition. 1-4 are all fairly solid (we don't talk about Dragon Quarter), but 2 and especially 3 are my favorites.

For PS1, I really used to enjoy Tomba 2 and Tiny Tank as a kid.

Shining Force 2 on genesis

King's Quest original series was and still is great

You can't go wrong with Sunsoft's NES library for the most part. Those are some of my favorite games on the system.

The first Phantasy Star is such a cool RPG, especially with the SMS Power patch that retranslates the game and adds several quality of life options.

Definitely give Top Gear 1 and 2 a go on the SNES. Outrun 2019 on Genesis is also pretty good.

Mega man 2, 3 (NES) and Megaman X (SNES).

The best driving game on the Atari 2600 - Enduro

I've been enjoying 30xx. It's a Megaman inspired game with lots of replayability.

Toy Story 2 for PS1, and if you like dragon ball you can try DBZ Legends for PS1 and Saturn, it is a short game.

King of monsters 2(?)