One of the weirdest games I've ever played: Okage: Shadow King.

Think Final Fantasy gameplay + Zelda: Majora's Mask level of being genuinely bizarre as all hell.

Fair warning, the music will be stuck in your head for the rest of your life.

Gauntlet: Dark Legacy is great classic fun

If you're a fan of the anime, the .Hack// games hold up pretty well. There's a little OVA that is included with each game to give more story.

Silent Hill 2

There are two amazing super hero games that I would recommend: Spider-Man 2 and Hulk: Ultimate destruction.

Spider-Man 2 was easily one of my favorite games of all time. This game essentially set the bar for what a Spider-Man game should be.

Hulk: Ultimate Destruction was an open world game where you were the Hulk and did all the Hulk things. I can't think of a recent game where you play as the green giant.

How is XIII via emulation? Would love to try that on my Steam Deck.

My entire childhood was Tony Hawk's Underground 2 on the PS2.

Jak 3

Arc the lad 2 twilight of spirits is a cult classic

...so grain of salt, cuz the name of this one doesn't sound right, but the screenshots look correct: Gradius V?

Side scroller arcade-y jet fighter - I remember it being good.

I just don't remember it being called Gradius >_<

Dark Cloud 2

Ratchet and Clank games

Dance Dance Revolution!

Soul reaver

Grand teresmo

Rayman 2

Ace Combat Zero! Or 4, 5, and Zero (in that order) if you want a lot of it.

Def Jam 2: Fight for NY. It's basically like some of the older WWF wresling games where there can be 4 fighters at a time, but you can only be targetting one at a time. But all the fighters are rappers. The finishing moves are awesome!

I absolutely loved KH1/2 FM

The Soul Reaver / Blood Omen games have not been recommended yet. Though, as a warning, last time I tried to do the Soul Reaver 2, there was a strange bug with the sound that made it so that you couldn't pass a certain puzzle.

Downhill Domination is... honestly stupid as all hell, but by design: it's a lot of fun :P

It's a downhill mountain bike racing game with a combat system, and it's ridiculous. You start being able to punch the bicyclists next to you; once you knock enough of them off their bikes you upgrade to being able to kick; then iirc you eventually get a stick or something lol. Otherwise, it's just another get-from-point-A-to-B-as-fast-as-possible game that doesn't require a lot of thought.

Primal.

Frequency & Amplitude:

The originators of the modern "rhythm game" genre.

Crash Nitro Kart and some of the PS2 Crash platformers are pretty good. The Kart one has a boosting system that I like better than mario kart (and better items and vibes tbh)

Definitely play the AC games. Which series am I talking about? Both.

Armored Core and Ace Combat are really good games. For the PS2 continuity of Armored Core it is arguable that the PSP versions are better due to the extra content, but otherwise it's not too big of a deal.