Just pick up a cheap rack server on eBay for a couple hundred euros. Something with a couple xeons, a decent amount of ram and a moderately sized HDD should be fine. For 10 players, I doubt you'd need to spend anything more than 200 euros.
Just install something like centOS on it, get ssh working, install your game servers on it, happy days.
If you're looking for cheap, this case is pretty small and relatively inexpensive. I was looking to make a minecraft server, and based on research this case is alright, aside from a couple of cheap fans that may need to be replaced.