Are these computer specs lacking for use with After Effects?

the 28 lane version i7-6800k could save some money if you don't plan on doing alot of expansion. 28 lanes can still split to x8/x8/x8 or x16/x8 on that motherboard. the 40 lane i7-6850k can split alot further, but depending on what you want for expansion options may require a better motherboard to split to 4 or 5 devices.

if 1tb of space is enough, you can switch to a samsung 960 pro or evo m.2 pcie ssd, which is faster than several sata ssd's. alternatively you could install os/apps on a smaller 850 pro and add a samsung 960 m.2 ssd for cache, projects, and media.

unless you are attached to the looks or some special function of that case, there are many cases around half the price that compete with it. some like the fractal design r5 have more functions, like noise dampening material to be quieter.