A single 16 slot garrys mod 9, or garrys mod 10 will run fine on something smaller, possibly a celeron 2.4ghz without issue. I spoke with garry the other day, he says linux binaries are a very low priority. You'll need to go with a windows server.
No I'm not banned Roflcopterrr, Don't see why I would be considering I'm a former FP mod as well as a former #gmod IRC op. Your most cost effective option would be to order a low end server from LayeredTech. Although I personally won't run a single GMOD server on anything less than a dual xeon since the srcds process seems to hardlock after being over 40% cpu usage for a bit (with gmod9). If the server is for Garry's Mod 10 the hardlocking should not be an issue, I spoke with garry about this and he told me that the hardlocking should not occur anymore.
yah, my guess is the fact that its a resource intensive mod, resulting in very little hosting of it by GSPs results in there being little requirement for linux dedicated servers. Most Garrys Mod servers are likely to be run by players on their own PCs and as such would be windows. However it would be nice to have least give it a shot on linux anyways :-)
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One thing i would suggest before you get a dedicated server is look for a provider who hosts steam games and put in a special request for gmod. More often then not, even though they may not have it listed, they will host it for you. Only thing i can see, is they may charge slightly more.
I do think you should consult this idea before you buy a dedicated server, although if you get a low end server, it may be cheaper, can't be sure.
From my experience with steam based games, is that it take alot more cpu then ram. You can definitely get away with 512mb of ram, as steam dosent use it much at all. As for the cpu, i would suggest going with a amd sempron or athlon, as they are usually cheaper and give better performance than their low end celeron counter part.
Another thing that could save you money, is see if you can find a host that will supply you with XP instead of server 2003, will help keep cost down, and you won't utilize the server edition very much anyhow.