"I plan to use it as a game server and web hosting server."
There is your first problem. I dont recommend mixing game servers and web hosting together.
"How much 8-16 slot counter-strike gameservers do you think a barton 3000+ hosting a few (less than 10, one relatively large PHP forum, 200 members, the other sites much smaller) can accomodate?"
With specs like that, and assuming your counter-strike servers will be public servers, I highly doubt that the performance of the servers will be good at all. Add the large php forum and a bunch of smaller sites, and the performance of everything will suffer. If you are still inclined to get such a low quality server (in game server terms) then I would just rush one 16 slot cs server and the other hosting that you have.
Well, it also depends on will you be using special commands (SYS_TICRATE or pingboosters) if so these commands increase cpu usage but also give the server a better quality. If you arent and you keep everything default, I would say a maximum of 2 16 slot publics or 4 private 12 slot servers.
F.Y.I. I am the type of person that cares more about performance than price