Generally, there are only 3 things you want to worry about when building a mining rig.

Graphics Card: This is the bread and butter for your rig and what is actually going to be generating your coins. Don’t cheap out on these
Power Supply: You will need adequate power to run your rig. If you are getting 2 or more graphics cards, don’t get anything under 750w. We’d even recommend 1000w+ in case you want to expand
Motherboard: The only thing you need to look for here are the amount of PCI-E slots (or places for your video cards). Try to find one with a minimum of 3 slots so you can expand if needed
The rest of the hardware doesn’t really matter.

CPU’s are virtually useless, you just need it to run the OS.
RAM, mining is not RAM intensive, so you don’t need to worry about it.
Hard drive, again, you only need it to run the Operating System.
Computer case, less is better. The less constricted your components are, the more air flows through and helps with cooling. Most of the rigs we build don’t even have a case.