Overall an i3 6100 does pretty well, you're not going to run Ultra 60+ fps "Which is what everyone on Tom's wants" but that is what you would expect out of a 3-year-old CPU with a resell value of $60. Will it Bottleneck a 1060 6gb? Yes at max settings you will see the same issues using any of the i5's in the 6th and 7th series as well. Best bet is to aim for an i7 6700, i7 7700 K or non K if you want Max everything and move beyond a1060.
As far as GPU's go look at the used market you can find 1060's starting at $135 with most of the Warranty remaining. I see used 1070's cheaper than new 1060 6gb with is also worth looking at.
Watch Dogs 2 and Witcher 3 I know will run on an i3 6100 @ 1080p High to Very High settings and stay above 50 fps without input lag or tearing. AC, on the other hand you would have to drop down to Medium to get the same gameplay experience.
I thought about used GPU, but cryptocurrency made buying used graphics cards hazardous. And warranty can be expired or don't last long enough.
@EDIT: Do you think that in RG4 case it will heat too much?
Most all 1000 series cards have a 3-year warranty.
1000 series launched in May 2016.. most miner cards you will find were bought 4-12 months ago.
Miners want to use the least amount of electricity as possible so cards are undervolted most of the issues are bad fans which are easy to fix.
Odds are it's fairly easy to find a card with a warranty if you look in the right places... eBay is not the right place unless you like overpriced pixel crack dealers. I would check Reddit Hardware Swap or a classified forum, the last 1060 6gb "$150" I bought off Reddit was a miner with 28 months warranty left, unregistered with the receipt.
If that is a Regnum RG4 case then you have plenty of Air Flow for all GPU's under 15 inches.