I would recommend starting off with an AMD A10-6800K APU, along with 2133MHz RAM to minimize bottlenecking of the onboard GPU. And as far as I know, the more you discover and build in Minecraft, the more RAM it takes. So it's good to have more than you NEED.
Here is the APU:
http://www.amazon.com/dp/B00CPLGGXM/?tag=pcpapi-20
Here is the RAM:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820226433
If you want to add a graphics card later, you will want at least a 500W power supply just to be safe. I would recommend one that's within your budget from Corsair or Seasonic.
The case is completely up to you, as there are different form factors to choose from. Let me know what kind of features you look for. I would also recommend getting a Seagate SSHD for storage, I currently have a 2TB SSHD, and it's pretty quiet for a mechanical hard drive, and the speed benefit from having an onboard SSD cache becomes more noticeable after the first several uses, even though I use it as a storage drive.