Will this motherboard work?

Here are better alternatives than getting the FX 8350 + AM3+ mobo (which are bad choices in this day and age due to its end-of-life status/no upgradability).

********** AMD RYZEN BUILD OPTION **********

PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Ryzen 5 1400 3.2GHz Quad-Core Processor ($158.79 @ SuperBiiz)
Motherboard: ASRock - AB350M Micro ATX AM4 Motherboard ($65.98 @ Newegg)
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-2666 Memory ($117.88 @ OutletPC)
Total: $342.65
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-18 01:34 EDT-0400

The Ryzen 5 1400 CPU is a 4-core/8-thread processor that can be overclocked. It only has a 65W TDP (compared to the FX 8350's 125W). The Ryzen 5 1400 has decent stock cooler already included in the box. This CPU, as of this date, is the lowest/most affordable CPU in the Ryzen series. This CPU is 20% better in overall performance than the FX 8350 (http://cpu.userbenchmark.com/Compare/AMD-Ryzen-5-1400-vs-AMD-FX-8350/3922vs1489). If you decide to get this build, it will allow you in the future to upgrade to more powerful CPUs such as the Ryzen 5 1500X/1600/1600X, or Ryzen 7 1700/1700X/1800X.

Among all Ryzen CPUs, the best price/performance is the Ryzen 5 1600 (6-Core/12-Thread) and the Ryzen 7 1700 (8-Core/16-Thread). If you can afford the Ryzen 5 1600 (it costs~$195), it's a better pick than the one listed above.

The B350-chipset motherboard is an AM4 socket/platform, which will support future AMD CPU releases. It's the best price/performance chipset as it allows overclocking any Ryzen CPU available as of this date. The ASRock AB350M has 9 Power Phases (good for stable OC'ing) and is one of the most affordable motherboards today.

The RAM required for this new platform is DDR4 (you cannot use older DDR3 memory sticks). Since the affordable ASRock AB350M only have 2 RAM slots, it is better to take advantage of dual-channel memory speeds by getting, at the onset, a 2 x 8GB kit (total of 16GB memory) so that you won't need to change RAMs in the future. You can, however, to save costs, opt for the 2 x 4 GB kit (total of 8GB), though, that is the bare minimum RAM capacity in gaming today.

Any of the Ryzen CPUs today will pair well and handle your GTX 1060 GPU.


********** INTEL BUILD OPTION **********

PCPartPicker part list / Price breakdown by merchant

CPU: Intel - Pentium G4560 3.5GHz Dual-Core Processor ($68.99 @ SuperBiiz)
Motherboard: MSI - B250M PRO-VD Micro ATX LGA1151 Motherboard ($61.99 @ SuperBiiz)
Memory: Team - Vulcan 16GB (2 x 8GB) DDR4-2400 Memory ($99.99 @ Newegg)
Total: $230.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-18 01:48 EDT-0400

The ultimate budget CPU, the Pentium G4560 is a great entry-level gaming CPU for a very affordable price. Despite the "Pentium" name, it can compete with the FX 8350 esp. in gaming/single-threaded applications. This CPU is 5% better in overall performance compared to the FX 8350 (http://cpu.userbenchmark.com/Compare/Intel-Pentium-G4560-vs-AMD-FX-8350/3892vs1489). It only has 2 cores, but with hyperthreading technology, allowing it to run on 4 threads. The G4560 is very low power-consuming/low heat-generating CPU with only a 54W TDP. It includes a stock cooler that can do its job (but it is not as aesthetically-pleasing and better-performing than aftermarket coolers available in the market). The G4560 is non-overclockable.

As the CPU is locked (non-OC'able), it is best and logically paired with a B250-chipset motherboard for price/performance. The MSI B250M PRO-VD is one of the most affordable and easy to use LGA 1151-socket motherboard that supports 7th-gen CPUs out-of-the-box (such as the Pentium G4560). It does not support overclocking. So, if you decide to get this build, you can upgrade in the future to more powerful CPUs such as the i5 7400/7500/7600 or i7 7700 - all non-OC'able CPUs in the 7th-gen series.

Among all 7th-gen locked i5 and i7 CPUs, the best price/performance is the i5-7500 (4-Core/4-Thread, no hyperthreading) which is very ideal as a gaming CPU and the i7-7700 (4-Core/8-Thread) which is ideal for both gaming AND multitasking/workstation CPU. If you can afford the i5-7500 (it costs~$188), it's a better pick than the one listed above.

RAM required is also DDR4 for this Intel build. Similar to the Ryzen build, if you can get the 2 x 8GB (total of 16GB), the better.

Any of the aforementioned i5 and i7 CPUs will pair well and handle your GTX 1060 GPU. The G4560 can also handle the GTX 1060 in almost all situations, except for very selected CPU-intensive games in worst-case scenarios (which you can easily resolve by decreasing in-game graphics settings).