Not sure if this is the right topic to post this kind of question on but I'll give it a shot anyways.
Basically I run a small steam group of ~260 members with a bunch of friends and we decided to host some servers. We originally just used Multiplay for a single Team Fortress 2 server but eventually cancelled it due to the fact that although it was sometime full to the brim we often had days when everyone was busy and the server was empty. So one of my friends suggested that I buy/rent a virtual/deditcated server and just host whatever game I want and switch whenever I please, the only problem is, I have no idea what I'm doing. I don't really know what's good and what's a ripoff price, hardware-wise I'm clueless, and with about a ~420 budget I was hoping I could get some help here. I don't really have any experience with hosting a server, nor do I have much experience with Linux but I'm more than willing to learn. Long story short, what would be my best option for hosting game servers (TF2, CS:GO, etc.) while being able to freely change them and what do I need to know?
Thanks :)