Minecraft usually requires a higher upload speed, but if your using for LAN or other games then that should be fine. It would be considerably cheaper just to build your own server, in a small mid tower case. Most game servers do not need a lot of cores, more so speed per core, with a lot of ram. They do not require a good graphics card as the CPU does all of the calculations for position data on the maps and damage details, etc, all the rendering is done on the peoples PC's who are playing the game. I would recommend a very cheap case, like a cooler maser elite, or some ultra case. For motherboards, I would go with a cheap AMD board on an AM3+ platform because first off, you could buy a cheap phenom II x4 and it would be enough 3.0 Ghz or faster, and when steam roller comes out and gives a 30 percent increase over bulldozer/piledriver, you could upgrade to even more performance if need be. The reason I recommended the Asus board is that most of their motherboards support ECC server class memory, if you are build a server that you will leave running 24/7 and need it to be fully reliable then thats a must. For video cards, you just need something that can boot into windows to set up the server, you can go with any 50 dollar graphics card, like an HD 6450, and it's more than enough, but never use integrated graphics as this eats up the RAM you need. If you need more than one ethernet connection, get a cheap card (so you can set one for incoming connections, and one for outgoing connections), and get 8 GB of RAM, ECC is more expensive, regular ram is only like 50. For a power supply, you would need a 400 Watt MAX as everything is low powered. All in all it'll be 50 for the case, 100 for the processor, around 80 for the motherboard, 50 for the RAM (I dont know ECC prices) 50 for the PSU, if you need a DVD drive get a lite on for 20, and for hard drive, you really dont need more than 120 GB as it's running game servers, so don't spend more than 80 on it, you can even spend 50, and another ethernet card ranges to 40 to 100. All in all thats about 420 bucks at best and about 500 at worst, and it has more upgradability, more expandability, can be used as a desktop on it's own, and it's just better in general.
If it's just minecraft I agree with scorpinock2. Minecraft can use a lot ram, you will have to find a way to get it to use ram effectively. More people on the server, more ram it needs to be able to use. If ECC provides better reliability for a server than go for it
The OS might cost something extra though. There are 320 gb harddrives that are cheap. You should back up your harddrive though, if you are using it for a minecraft server. You don't want your harddrive to go kaput and lose everything everyone built right?