Google for "game servers" in your country. There are usually dozens of companies specialising in game servers and they normally charge per slot on the server.
If you want to make your own, look for a full dedicated server (not a VPS - virtual private server). You're looking at a bit more money for that though.
I used to run my own Counterstrike server on a dedicated Linux server and it used to cost me about £100 year. Good luck finding it for much cheaper, because it's usually classed as a high CPU / high mem / high bandwidth application and thus you'll incur charges or problems if you just use a cheap host that doesn't realise you're hosting games.
P.S. If you're only running it as a Game server, you'll be better off with a Linux server. It takes literally minutes to install a Steam server on Linux (I suggest you practice on an offline Linux machine first) and costs a lot less because it doesn't need your host to buy a Windows license. If you're not up to that, you're going to want to be buying a managed game server anyway, from a specialist company.