i3-6100 nearly 50% more single-core speed. And with the FX-8350 using four cores, it's still 6% slower than the i3-6100 according to some benchmarks. Only time it beats it is when it uses all 8 cores, which not all games do.
So you are paying more and it isn't better at everything. Not to mention the FX-8320 is the same chip and just needs a bit of overclocking to be the more expensive FX-8350.
A Skylake i5 + budget motherboard may have been a better choice with your increased budget.
With the Spec 01 case, remember to pass the 8-pin EPS cable from the PSU (for CPU power on motherboard) through the hole in the motherboard tray, before mounting the motherboard. There isn't much room at the back for cable management at all, so recommend zip-ties v velcro in this case and being creative (i.e. use all the holes you can find to position zip-ties in other places to spread out the cables more).