It really depends upon what operating system(s) the games you want to host are written in. From what I understand, most games that are server based will run on any operating system - but there are a few that require either Linux, MAC or Windows based OS. Linux & Microsoft are going to be the two most stable environments - with Microsoft being the more familiar to Windows users. Linux servers host a majority of the web and gaming platforms - due to cost and resource management.
Linux servers will run on virtually anything out there - from an old PC to any server based hardware. Microsoft Server (2008, 2008R2, 2012, 2012R2) are going to run best on server based hardware - but will run on virtually everything.
Windows Server will run about $600 (you can find some on eBay for less) - and Linux is free.
Server hardware - specifically a Dell 2950 with 32GB or less of RAM are going pretty cheap - eBay is littered with them for about $200-$300 - and some come with the OS license.
It comes down to money in most instances - are you willing to spend the money for the Microsoft solution, or do you want a "cheap" (not meaning loss of quality) solution.