Parts of a Bitcoin Mining Rig Original question: How important is a strong CPU and GPU for ASIC mining? I would assume that the GPU could be a cheap one because even if its high-end it probably won't help, and that the CPU should be a decent one to handle all the ASICs. Am I incorrect?

In addition, what is the importance of each part of mining computer in terms of mining? How do the Motherboard, CPU, RAM and GPU affect your experience?
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.