Half-Life series, Doom, Bioshock series, Deus Ex series, Superhot, Lovely Planet, Hotline Miami 1 or 2 to name a few. Honestly go with games you've played and enjoyed, give the run a look, and see if that looks like something you'd be interested in putting time into learning and running.
I'd recommend any Call of Duty game that isn't a Treyarch game. While Treyarch is my favorite of the 3 developers, for some reason their game seem to break super easily when ran too fast
FPS's kind of fall into two categories: Objective/level completing, or DM/arena/bothunting.
Examples of Objective/level completing would be the call of duty series or the doom series. Basically FPS's where there are no set amount of kills or rounds. In order to proceed to the next map, you have to get to the end of the map you are currently on. There can be minor or major objectives that have to be completed to get to the end of the map, but it is still a "Start---->End" sort of scenario. Doom, CoD, Wolfenstein, time splitters series, and Halo are some examples of games that come to mind.
DeathMatch (DM) or bot hunting or rounds or whatever you want to call it is the Unreal Tournament and Quake III Arena style of play where you have to get to a certain Frag limit or kill all of the enemies on the opposite team a certain amount of times in order to move on to the next round and/or map. Unreal Tournament 99. Quake III arena, Quake III Team Arena, and the Counter-Strike games would fall into this category.
It depends on what you are looking for, and some FPS's can fall into both categories. Counter-Strike does have objectives (like rescuing hostages and disarming bombs), and UT99 has the domination, capture the flag, and assault game types that allow you to do a lot more than just fragging. I have done runs in Counter-Strike Condition Zero, all categories of UT99, and I am currently working on Quake III arena. All three of those games, even in their most competitive categories, still have room for improvement with regards to their various wr's. Like bullets said, find a game you like and try it out a bit or watch some other runs to see if they are your cup of tea.