Game server on a budget any input would help

My friend wants me to build him a game server for Minecraft / DayZ, and for a few other simple tasks. I am not new to building PC's but this will be my first game server, was wondering what I should go with for about 800$ budget and if I should use a SSD in the system. I am thinking of going with around 16-32 gigs of ram and amd 6-8 core for the system. I also have a AMD Phenom II X4 with 8 gigs of ram sitting around with a 5770 in it and was wondering would that work him for a small Minecraft server.

Game servers are essentially just gaming machines, but without the GPU.

Minecraft thrives off of as a fast as possible CPU or a cpu with a high IPC, a lot of RAM (but entirely depends on size of world, number of plugins, number of players and finally a high speed access to storage. So an SSD is ideal.

As DayZ uses a static world its not important for a fast storage device. I'm unsure on how much RAM it likes to use, but it can't be too much, again due to a static world. It would require a fast CPU again, but that might be possibly offset depending how the server side of DayZ is scalable to multiple cores.

For an AMD system you could do something similar to what is on my profile. With an FX-6300 OC'd to a faster core clock.

But more importantly than the system, is your connection speed and latency. Unfortunately no matter how fast the system is, the overall experience will be crap if over a WAN if it doesn't respond fast enough.

An Intel chip would help a bit for a minecraft server, due how Java is shit at multiple threads.  16 gigs of RAM would be the minimum.

Thanks for the input now I just need wait for my friend to give me his final budget so I can order and build the server for him.