I say Windows because it's built more for gaming and I am a gaming type of guy. Like Linux is better than MAC for gaming as well but Windows is like the bootleg version of Windows but still is good.
It varies if you're using your computer for gaming windows would be your best option. If you're using your computer for server hosting consider linux. I personally use Windows. Windows is the most efficient because its easier, faster and overall more secured than linux.
First of all , please clear your question but telling the games , many games are just for windows environment , but if those games are for linux too than you can surely go for linux.
Depends on setup. Are you trying to host on the same machine you game on? Are you renting, do you have a secondary machine? If you're hosting for home, what's your network, etc.