After a short delay, the gaming PC is a go and the parts are on their way. The delay was caused by a general shortage of Intel Skylake architecture CPUs. Everywhere seemed to be sold out, and the places that weren’t seemed to be marking the prices up as much as 50%.
I just waited a bit and, eventually, was able to find a reasonably priced, in-stock bundle of my CPU and motherboard choices at NewEgg. The rest quickly followed and now I just need to wait for the stuff getting shipped from New Jersey. While the guts were all priced cheaper and were more likely to be in stock at NewEgg, it turned out that the OS and peripherals were better to get from Amazon.