Cheapest CPU+Mobo combo you can find with desired number of PCIe slots (if it's still in production it will work fine, assuming you are mining on GPUs).
2 GB RAM.
16GB USB Stick for linux distro of choice (hard drives cost more and use more power).
Power switch
Powered USB PCIe risers
If you are mining a CPU coin you will probably want a better CPU.
2gb of ram is not enough. If you are mining with 6+ gpus you might need at least 8gb as I have read that some ppl have problem with 4gb
Additionally, for some miners, additional storage may be necessary for page file/swap. For example, Claymore suggests having a minimum of at least 16GB of virtual memory for multi-GPU systems using his Zcash miner.
I would avoid using a cheap flash drive as a boot disk for long-term 24/7 use when you know a SWAP partition will be needed. Generic USB 2.0 drives can often wear down quickly. Quality flash drives would probably be okay.
I've just been putting some of my old 80GB SATA drives to use. Regardless, ensuring that you make a full image after setting up a working configuration can save you a lot of trouble, should something happen.
Extra tip on powered risers: SATA powered PCIe risers are generally not recommended, since SATA connectors are not designed to handle the current. Risers powered by 6 pin PCIe power connectors or 4 pin molex connectors are generally safer options.