So many nice recommendations here but here are some of my recommendations in genres (in top 5 form). All of them have PC ports (but not all of the series may be available on PC)

Platformers:

1. Rayman
2. Sonic
3. Wonder boy
4. Shantae
5. Trine

RPGs

1. Final Fantasy
2. Tales of Series
3. Star Ocean
4. Elder Scrolls
5. Pathfinder

Some noteworthy mentions for RPGs

1. YS
2. Mana

Shooters:

1. Medal of Honor
2. Shadow Warrior
3. Doom
4. Call of Duty
5. Wolfenstein

Puzzles, point and click: Note: This was very hard to list since most of them are standalone and those that are not have interesting plot lines that you will not appreciate unless you play in order such as Syberia, Gabriel Knight, Secret Files. Walking Dead)

1. Myst (You can play in any order but it would be nice to play the sequels or prequels)
2. Broken Sword (Don’t touch 4 and 5 but you can play in any order and it would be nice to play the sequels or prequels)
3. Life is Strange (1 and 2 are standalone stories)
4. of Loathing series (It has turned based combat but very fun)
5. Nancy Drew

I would say I prefer them in the chronological order of their release date. Some of the series I have listed completely have either loosely, small references or completely standalone only sharing a “franchise name”

Two reasons.

One is the form factor.

While certainly my ROG phone plus gamesir is enough to even emulate this gen’s handheld games. It cannot beat playing a gba game on an Anbernic rg35xxsp.

Second is that some owns a low tier or a very old phone and they don’t want to throw it away because it still works perfectly fine.

So instead of spending 300 bucks for a decent mid tier phone replacement, plus accessories, spending 99 bucks is far more cost effecent.

Then there is that storage issue. Some newer phones today no longer have an sd card slot for expandable storage.

Plus some if not all of these handhelds are moddable as fuck too.