I can't answer anything about the wireless, as I have never used wireless before.  (I have no need for it)
I personally use Slackware Linux on my server. 
I have used Mandrake and Redhad in the past for the same purpose.
I have played with OpenBSD and FreeBSD,  but my knowledge is VERY limmited with them.
My server is my router/firewall
I also use it as my ftp server (proftpd), web server (apache), local file server (samba), 
I used to use it as a DB server,  but I no longer  need that functionality,  so I don't have PostrgreSQL on it (since I switched distros)
I also use it for some non-server type things 
-- I use it to connect to IRC (I run BitchX on it for that,  I connect to it from my other PC in a putty ssh window.  Been using BitchX for a long time now,  maybe 5 years or so,  and don't have any desire to switch to any other IRC client)
-- I run X.org on it with fluxbox ... it's sometimes handy just to have as a websurfing box.
I'm running a 1.8ghz Celeron with 384MB of ram.  It's more than enough for what I use it for now. 
If I didn't care about getting X to work,  I would probably be OK with a P133 and 64MB of ram (well, except maybe not due to possible issues with drives > 137GB)
Some will say Linux Distro "?????" is the best,  others will say FreeBSD, others NetBSD, and yet others OpenBSD.
You should first decide,  
Do you want to use "iptables",  "netfilter" or "pf" for your firewalling and nat?
for Web Server,   apache runs on everything
For File Server,  Samba works great in Linux (easy as pie to set up with SWAT),  I hear it works equally well on *BSD
For Print Server,  Samba does that too ..
For PVR,  look up "mythPC"  It was designed for Linux,  but there may be ports to BSD's ... I don't know 
You're gonna have to just pick something and stick with it ... or you're going to really need to reseach quite a bit.
There are many good options here,  and everyone seems to think theirs is the best.
OpenBSD is kinda picky when it comes to hardware,  but it runs with most stuff out there.  (Linux is the least picky about hardware,  but the quality of the drivers is not always top notch)
Personally,  I would avoid redhat (or Fedora as they call it now),  I find they bloat things up a bit too much.  They try to make everything too "idiot friendly" and they generally leave lots of things "open" that generally, you don't want to leave open.
I'd go with Slackware,  ohh wait,  I already did 

      (Otherwise Gentoo, Debian and, Ubuntu seem to be pretty popular these days,  so support would likely be plentifull)
My second choice would be OpenBSD,  it really appeals to me a lot,  I'll eventually toss together a BSD box just for kicks ...  (assuming you don't need the PVR,  or you find something that works in OpenBSD for that purpose)