The i3-6100 is a solid choice. I have one with a GTX 970 and while I can see where it bottlenecks performance, 60FPS @1080p on 97% of games is not unheard of. I do get a predictable drop to the low 40's in certain parts of the city in GTA 5, with heavy traffic (both vehicle and pedestrians) so I just play at 1323p with most settings maxed out (reflection MSAA, high res shadows turned off and particles on medium) and still see 60FPS most of the time with vsync turned on.
If I catch you before you buy, get a reputable brand Z170 motherboard. Some still allow non-K skylake overclocking (do some searching) and with higher speed RAM available with the Z170 boards, you get a pretty substantial boost in performance with weaker processors like the i3 and Pentium Skylakes.
I thought 2133Mhz was plenty, because most people are running DDR3 1600Mhz but benchmarks prove time and time again that the i3-6100 with 2400Mhz DDR4 or faster is good for a constant 2-5FPS boost. Overclock it to 4.4Ghz (very stable from what I've read) and you get an even better boost. All you need is something like a Hyper 212 Evo cooler to keep the CPU cool (which shouldn't be hard) and you can get easily close the gap between the i3 and it's i5 bigger brothers, possibly run even better until you get to i5-6500K overclocked levels.
I bought an H170 board because it was on sale and now realize that I just bought a Z170 board without the faster RAM ceiling and overclockability. If you don't plan on overclocking, jump down to a quality H110 board to save some money as you will see no performance loss as long as it has all the features you want.