Some offline-friendly FPS games.

• Half-Life 1 and 2
• Borderlands 2 and 3
• Dusk
• SEUM: Speedrunners from Hell

First-person puzzle games (other than Portal 1 and 2, which you've heard about enough already):

• Once you're done both Portals, check out community-made mod campaigns!
  • Portal: Revolution is a prequel to Portal 2 that introduces a few new mechanics.
  • Portal Stories: Mel has pretty much zero new mechanics but cranks up the difficulty.
• Viewfinder
• The Witness

Not one of the types you were asking about, but Hades feels like it's made for the Steam Deck, and it's a great game (and also on sale)

For FPS games, Doom (2016) is one of the all-time single-player FPS games and runs great on the Deck.

Stardew valley, Midnight sun, diver Dave, persona 5

Try these gems:

• Vampire Survivors
• Death must die
• Dead Cells
• Animal Well

It's as if they were made specifically for the Steam Deck

Half Life 2 and it's episodes are always on a massive sale in a Valve bundle.

https://store.steampowered.com/bundle/232/Valve_Complete_Pack/

There's a lot of stuff there you won't play, but it's a must have for the Half Life and Portal series.

Also Wolfenstein: The New Order and Doom 2016 are great.

For Elder Scrolls, I'd recommend giving either Oblivion or Skyrim a whirl, and then after you feel done with one, try the other. In my opinion they are both great for different reasons, and they are different enough to feel like very different games in some ways.

If it helps you make a decision in terms of RPG story feel, Skyrim is more about you as the hero, and Oblivion you're more like a person that happens to be there.

There's great modding resources too if you're into that. Especially on Nexus. Even light modding like some QoL upgrades or bug fixes. I'm not talking crazy mods.

Oh, the endgame for Skyrim (the original DLCs) really do give you some rewarding post-game fun in like a god mode.

The Halo Anniversary collection shines on SteamDeck. It was my first purchase after getting mine, I think.

Monster Sanctuary! Outstanding mix of metroidvania and pokemon sorta game

Vampire The Masquerade Bloodlines

Not sure how it plays on Deck (UI is pretty small scale iirc) but Morrowind is great if you like RPGs with great atmosphere that don't hold your hand, and if you're ok with oldish graphics (some famous mods make it much more palatable however). I don't particularly like Oblivion or Skyrim, they're much more generic whereas Morrowind is pretty unique in terms of universe. But then again you'd have to look up how well it runs on the Deck and whether or not you can install the unofficial bugfix mod among other obligatory things

Shadow of war is 2.99 CAD

In case RPG includes JRPG for you: Both Nier:Automata and Nier:Replicant play fantastic in the deck, and those games are far more enjoyable with a controller instead of keyboard and mouse

Cat Quest

RPG wise all the dragon age games are on sale, plus there's always fallout or skyrim.