Parts of a Bitcoin Mining Rig
The hardware of the controller doesn't matter. You can run cgminer on a Raspberry Pi or a TP-Link router, both are terribly weak and it has absolutely no effect on the ASIC whatsoever. To this end, even KNC mining rigs use Beaglebone Black boards to control their top of the range miners. Most home miners use Raspberry Pi due to their low cost and easy to run software like MiningPeon.

CPU, memory, GPU are all largely irrelevant.