I know I can't answer without more details (games being hosted being the biggest). However, assuming these are Windows-based games and are relatively modern, I do think Windows 10 would be a good fit here. It would fit well with your Microsoft account, and runs very well right after install. On the one I use as a file and media server, I personally go through and remove some of the auto-install bloatware that comes with a fresh install, and restrict some personalization preferences, but that is probably more user-preference than anything.
I will say that for my purpose, getting Windows 10 up and running on my server took much less time than it did when I was running Server 2008 R2 for a time, mainly because I had to customize a ton of things that didn't apply since this was a home, and not a business network. So it really all depends what the server is going to be doing/ how you are going to be interacting with it.