The PSP is not a great platform for first person shooters in particular due to the lack of a second analog stick. There are a handful of quality third person titles though, chief among them the two GTA Stories spin-offs set in Liberty City and Vice City. These are proper classic 3D GTAs, just as sophisticated as San Andreas, but set in modified versions of the cities from the two predecessors. Both assume that you have played and completed GTA 3 and Vice City. These spin-offs were also available for PS2, but the PSP versions should run better and can be made to support a second analog stick in PPSSPP:

https://github.com/Freakler/ppsspp-GTARemastered?tab=readme-ov-file

While you're at it, you should also check out the isometric GTA Chinatown Wars, a unique and extremely well made title that straddles the line between 2D and 3D GTAs, but with game design that is as modern as GTA IV's (but far more arcadey). It has been ported to Android, however, the PSP version is superior, having better graphics, more features (including multiplayer) and more missions.

One genre that truly excelled on Sony's little system was racing games. Here's a list of highly recommended titles of all subgenres, from arcade to simulation, that I compiled a while ago: https://beehaw.org/comment/2784912

Note that Gran Turismo can be patched to support analog throttle and brakes: https://github.com/Kethen/RemasteredControls_GTpsp

Now, on to the PS2 shooters:

• Scarface: The World is Yours. Perhaps the best clone of classic GTAs, to the point that it's the superior game in many respects. From the developers of The Simpsons Hit & Run, but decidedly less family-friendly. Brilliant graphics for the platform, outstanding voice acting, writing and direction. Watch the movie first, if you haven't already! This very late licensed title boasts a fantastic combat system that is all about targeting specific body parts with perhaps the single best lock-on system in gaming history while hitting a button for swearing in order to fill up your "balls" meter, which, once full, allows you to switch to a first person mode with invulnerability and unlimited ammo. Combat is mad, bloody, unhinged fun. It's not just presentation, narration and combat that are good in this game: There's are really well made empire building mechanic, a negotiation minigame that somehow never gets old, some clever risk/reward incentives for players that remind me of roguelikes, a good (if not quite as good as GTA) open world, a catchy '80s soundtrack. Lots to love about this game.

• Black: Criterion (otherwise known for the Burnout series) tried their luck with a first person shooter. It shouldn't have worked, but they somehow pulled it off - and it's just as wild and explosive as the racing game series. Every single weapon, from the lowliest pistol, is loud, punchy, powerful and sends the hapless enemies flying. There's a marvelous destruction system that feels like black magic on hardware as old as the PS2. The story is nothing special, level design and scripting are average (but levels are at least fairly large and quite open at times), it's not particularly long nor deep and there are difficulty spikes, but overall, this is still one of the most enjoyable first person shooters on the system and one that holds up remarkably well.

• XIII: Based on a popular Belgian series of graphic novels, this highly stylized first person shooter has become a cult classic over the years. If you like conspiracy stories, cell-shaded graphics and a seamless blend of stealth and explosive action, then you will enjoy this game. Best feature: The kill cam, which consists of comic book style freeze frame inserts. So satisfying! Check out the comic book as well, while you're at it. Just keep in mind that it's far less stylized and far more adult than the game.

• Timesplitters: I haven't personally played this series yet, but since it's by former Rare developers, the same people responsible for Goldeneye and Perfect Dark, and extremely highly regarded, you should probably not pass it up. Note that the second and third game are also on Gamecube and will likely run better in Dolphin than the PS2 versions do in AetherSX2.

• Deus Ex: The classic immersive sim does qualify as a shooter if you choose to play it that way, but you're far better off playing it slowly and meticulously as a stealth title. The PS2 port is very interesting. In some ways, it's compromised, with slightly simplified graphics and levels having been broken up into smaller chunks due to memory constraints, but on the other hand, there is added detail to the environments and animations received a motion capture overhaul. There's also a completely different UI. If you haven't played this absolutely legendary title with sheer endless depth, complexity and replayability, then definitely give it a go.

Gamecube/Wii:

• Metroid Prime Trilogy: Sci-fi 3D Metroid goodness. I have to admit that I haven't found the time and patience to really sink my teeth into these games yet, having only perfunctory experience with them, but there's no denying that these are outstanding games, with strong, inventive mechanics, complex level design and excellent presentation.

• Resident Evil 4: The best console version of the original classic. The PS2 port was severely compromised, as was the original PC port. Note that on PC, you can install the RE4HD project, which is perhaps the most impressive fan remaster of all time. The developers of this mod even traveled to the locations that the original developers used for reference photos in order to capture material for enhanced textures and geometry. There are texture packs for Dolphin, which are however, to the best of my knowledge, nowhere near as in-depth. Still a decent way of experiencing this title though.

• Gun: Neversoft's attempt at a third person open world Western game. A solid effort. Compared to Red Dead Redemption on Xbox 360 / PS3, it feels like amateur hour, but it's still fine, with good combat, limited exploration and a solid story. The open world is unfortunately not very open, hampered by invisible walls and fairly bland design.

• James Bond: From Russia With Love: An unusual licensed title, based on 1960s James Bond with Sean Connery, dripping with atmosphere, charm and spectacle. There isn't much depth here, but it looks great, plays fluently and is solid fun all around. If you like the idea of racing a classic Aston Martin through dense European streets in one level and fighting bad guys while being suspended from a jet pack in another as Sean Connery does his best to charm some hapless bond girl, then check this game out.