The PoP games are borderline unplayable on a modern widescreen monitor and a modern OS. I have them all and it's a struggle to play, controls are funky, resolution issues etc. Wouldn't recommend, even if the core gameplay is good.
There are mods that fix them.
https://www.pcgamingwiki.com/wiki/Prince_of_Persia:_The_Sands_of_Time#Widescreen_resolution
https://www.pcgamingwiki.com/wiki/Prince_of_Persia:_Warrior_Within#Widescreen_resolution
https://www.pcgamingwiki.com/wiki/Prince_of_Persia:_The_Two_Thrones#Widescreen_resolution
I played them with Kb + M and I never had any trouble. I have a vagu memory that the default Mouse camera is vertical and horizontal inverted in warrior within. But you can change that in options.
Sands of Time - Warrior Within - Two Thrones is a good trilogy. The endings in each are fulfilling, so you don't really need to play the next one, but you should still play them in chronological order as WW and TT refer to past events.
SoT is the best game in the series.
Haven't played the 2008 reboot, but I heard it's okay.
Forgotten Sands is mediocre from what I heard and it is where the series died (and was replaced with AC).
Sands of time is the one that introduces a lot of the mechanics in the trilogy, but combat is simple and a bit repetitive, but it never overstays its welcome, and the game folows a linear level by level system. Warrior Within changes the tone into a more edgy presentation, with another voice actor for the prince, but combat is more elaborate with different weapons and combos, it is in a way a metroidvania, as you can backtrack and the whole island and unlock ways to progress, and explore places in the past and the present (but there is missable areas wich may affect the ending - you have to explore a lot to get to all areas and get a final item which unlock the best and canon ending). The two thrones comes after the success of god of war and since the POP and GOW had similar gameplay, they added a whip/chain like weapon like kratos blades, but it gets back to the tone of the original, even bringing back the original voice actor, but combat improved from warrior within. It's quite linear again, level by level. The story is all interconnected and the trilogy ending reminds me a lot of the thief trilogy ending, in the sense of closing a cycle.
POP 2008 is a stand alone game, using assassin's creed engine, and it has a whole new setting and setup. It has the infamous "you can't die" mechanic. It's is a good game, it's really beaultiful, but it's incomplete on PC, since it doesn't have the DLC that adds the epilogue. The platforming is it's strength, but combat is bad. I wouldn't recommend this, only as a curiosity.
Forgotten sands came at the same time they released the prince of persia movie. It is set between sands of time and warrior within. It's good and it improves the time powers in ways the originals couldn't, and if you liked the platforming and traps of the trilogy, you'll enjoy. But combat is again, terrible. they used Assassion's creed engine again, and one of the features of that game was the ability of rendering crowds. So the put you aginst dozens of enemies at once, but they are so slow and telegraphed that they offer no challenge at all. Also, this game is a filler, adding a brother to the prince that was never mentioned before, but all in all, it's better than the 2008 game. I would recomend for the platforming alone.
There's a nintendo wii/PS2 version of forgotten sands, that is not a port, but a whole different game that has the same story of the main game. but I never played it.