To be honest, Linux would be your best bet. Especially a Linux Server, because that will slow down your system the least. However, provided you have hardware powerful enough, you should be fine. I would definitely use Windows 7 if you're not going to use Linux, but go with Home Premium, as it's going to be the cheapest.
I'd be very worried about your ISP though. How many players do you plan on having on your server concurrently? Also, what ISP do you have? Some ISPs are known to throttle your connection if you're consistently using a lot of bandwith. I'd be careful, and maybe even look into co-hosting.
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Space