I looked at AMD (X4-860K) but I only save about $30 due to the motherboard and cost of DDR3 memory. It's still 10% of $300 but not really the best way to go.
I don't know how good the Gigabyte linked above is for the i3-6100 but it at least has a Warranty, nor can I find evidence that it will have major issues.
The i3-6100 wins over the X4-860K in all scenarios (unless you use all threads nearly fully and overclock the AMD CPU enough).
Long story short, I do think this is your best path to go. Some more tips:
Installation:
1) Build PC
(optionally, but recommended is to run Memtest86 www.memtest86.com to test DDR4 memory sticks)
2) Insert W10 install media (USB or DVD)
3) Install
4) Let MS Updates finish (manually check)
5) Install video drivers (If MS did already reinstalling won't hurt). Get direct from NVidia site for NVidia cards.
6) Download motherboard fan control software if available and setup fan profile for CPU (and possibly case fans if applicable). You can navigate to the site for your EXACT model of motherboard. May have some software on a disc but generally go to the site first. If unsure, don't apply updates.
7) Motherboard BIOS update if newer exists
8) Install Steam, register account
9) Other programs:
a) Antivirus (some okay free programs)
b) Faststone (images)
c) K-Lite Standard (video)
http://www.codecguide.com/download_k-lite_codec_pack_standard.htm
Other:
a) Intel CPU diagnostic:
https://www.google.ca/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=intel%20cpu%20diagnostic
b) Intel driver app check: https://downloadcenter.intel.com/