First off, List is flawed by the lack of 3 of the greatest first person shooters franchises in the name of half life, BioShock, and borderlands. That alone shows severe lack of knowledge about the best series in the genre.
Secondly, fallout is not a fps. It's a western role playing game with shooter elements. That's like calling meroid prime aa fps. Metroid prime is a first person adventure game with shooting elements. The end goal of metroid prime is to explore where as Fallouts end goalgoal is to explore a world and role play in it. First person shooters tend to focus around the killing of enemies over other hand play elements, where as it is possible to kill very little in the newer fallouts.
From the list though, I'm picking team fortress 2. Easily accessible, fun, free, and suited for all types of play sessions.
The shock series also used to be fpa's. At least until infinite.