if you have money, destiny 2 is fun.
rainbow 6 siege, quake champions, hell even Cs:go is still fun and tf2
Team Fortress 2 is fun
Quake Champions for pure pvp fun.
If you want some great PvE with amazing devs, then Warframe is the way to go (though it’s not first person). If you feel like getting scammed out of your money, then I recommend Destiny 2.
I find paladins to be fun i especially like their support class
realm royale
h1z1 - only on ps4
TF2 definitely. It’s free too.
Original Halo trilogy. My favorites of the FPS genre, too bad the multiplayer for the MCC isn’t too active.
minecraft survival games
In my opinion, all of the best PvP games are dead. Lawbreakers was amazing and had the potential to be better than Overwatch, at least for FPS fans, it did not have any of the boring stuff in Overwatch to let the MOBA fans compete. Gotham City Impostors was excellent fun, just so unique.
As for PvE, someone was joking with Metroid Prime, but seriously, it is the best trilogy in gaming. If you have never played those, I could not recommend them more. A lot of people brought up Borderlands 2. Borderlands 1 is low-key superior, at least if you do not care about the narrative. I will even add Prey into the foray, if you enjoy horror. It is relatively new and the launch was a bit shaky, but if you enjoyed Prime, it takes that Metroidvania approach and mixes it with Dead Space. And yes, Doom. Can’t go wrong with that.