I'm on a budget and building a gaming PC, is Linux at all useful in this application? Will I be able to play with people who have Windows?
Answer to the question
Basically this is a very broad question with a lot of variables. But a short answer is yes, you can game on Linux. Will you be able to play with people who have Windows? Yes and no, depends on the game. Basically you won't be able to play everything on Linux that is on Windows, but there will be a pretty good selection and it is constantly growing.
Long answer is yes you can play with people on Windows (or Mac) if you can get the game running on Linux via Steam, Desura, WINE / PlayOnLinux, or some other options mentioned here. There are also games that you can just install without needing Steam or another program. If you can't find the game on any of those resources, chances are that you cannot play it. But having said that, there is A LOT of games available on Linux and the list is growing constantly. I currently use Ubuntu 14.04 LTS as my main Operating System, and I play a lot of games natively under Steam (Dota 2, Counter Strike Global Offensive, Football Manager 2016, Arma 3, some of the Total War series, etcetera). Even my 144Hz gaming monitor runs on Linux with the cool feature known as LightBoost. There are some games I cannot play on Linux natively, and thus need WINE / PlayOnLinux to run, but I have had mixed results with performance that way. You could also dual boot Windows to play Windows specific games, which is what I do to play DayZ Standalone. Hope this helps =)