1:Which distro would be best for a gaming server?
it doesn't really matter...a distro that supports glibc 2.2 or 2.3, which is about all of them right now.
2:Would I have to emulate Steam and a dedicated server through Steam in order to do this? Or would it be a different non-Steam way?
just download and run this file, this will get your dedicated server on steam...http://www.steampowered.com/download/hldsupdatetool.bin
3:Would it be free? I have a T3 connection available, so, I'm wondering if I would need to pay for any of this.
it does NOT cost anything to run a Counter strike (source or 1.6) dedicated server.