Deep Rock Galactic - is awesome actual coop team-play shooter (team matters)
Have many unpredictble cool team situations and fun shooting mechanis
can be boring in singleplayer - have servers list and matchmaking
Warframe - very good relaxing shooter game with action RPG elements
A lot of content (weapons, skills, pets, build modifications, fashion, craft, unique game mechanics)
If you like to Collecting stuff and shooting - you will get greate enjoy
Game is very easy - but Learning Curve can be intimidating (what to do, how, and where)
Game community is giant and very helpfull
anyone wants to help you and will answer any questions any time
* repeating map areas and same mission types can be frustrating
but there always have different things to do and break repetition loop
* game also fully free - any game stuff can be obtained through "playing the game"
Dying Light - nice Zombie with Parkour movement game
Singleplayer or coop - played in story campaing with nice length
almost all weapons is Melee - Firearm will be later in game
Interesting and fun to run with friends
Good as simpleplayer game too
Destiny 2 - AAA game with gorgeous graphics and excellent first person shooting mechanics
Have story campaing - but mainly work around static areas with AI enemies (and instance missions)
* will eat your wallet and all your saved money
* Developers commonly do inadequate updates
maybe in final version not even possible to play old big story campaing
* But it have free version with limited content
Try it for sure - game have many great and bad things at same time
Monster Hunter World - Singleplayer or Coop in same world and maps (1-4 players)
If you like deep Melee mechanics like in Dark Souls - you will love it
Game about Hunt on Giant Monsters
Each session is kind of unique and goes 10-50 minuts with pure enjoyment and action
* also have shooting weapons
* best played with friends
Singleplayer or game with random matchmaking can be boring after sometime
* Whole game is about "Collecting resources to Upgrade Gear" Concept
If you want deep story - this is wrong game
PS.
Valaetoshiru - you not specified what you actually like and want in games...