The differences in FPS between a Ryzen 5 and i7 7700k with any main stream video card is very little. The 1600 for $199 comes with a decent CPU cooler. It offers the best bang for the buck, and will overclock the same as the 1600x. 3.9-4.1GHz depending on the silicon lottery! Also, the CPU load playing games will be less on the 6 and 8 core systems while gaming. Ryzen 1800X has been tested to be better than Intel systems including Intel's 8 core 6900k when it comes to streaming games. The 1700($299) comes with a CPU cooler and can overclock to be as effective as the 1800x. Also, AMD will be using the same socket, so you can upgrade to the next generation Ryzen CPU that comes out next year.
Motherboard
$79.99
$74.99 after $5.00 rebate
ASRock AB350M Pro4 AM4 AMD Promontory B350 SATA 6Gb/s USB 3.0 HDMI Micro ATX AMD Motherboard
2 M.2, Type-C, Triple Monitor, ELNA Audio, LED
AMD Promontory B350
A-Series / Ryzen Series
Ryzen series CPUs support DDR4 3200+(OC)/ 2933(OC)/ 2667/ 2400/ 2133
7th Gen A-Series APUs support DDR4 2400/ 2133
https://www.newegg.com/Product/Product.aspx?Item=N82E16813157762
CPU buying choices
AMD Ryzen 5 1400 Processor with Wraith Stealth Cooler $157.49
https://www.superbiiz.com/detail.php?name=YD1400BOX&c=CJ
AMD Ryzen 5 1500X Quad-Core 3.5GHz Socket AM4, Retail $176.99
https://www.superbiiz.com/detail.php?name=YD150XBOX&c=CJ
AMD Ryzen 5 1600 Six-Core 3.2GHz Socket AM4, Retail $199.99
https://www.superbiiz.com/detail.php?name=YD1600BOX&c=CJ
AMD Ryzen 7 1700 Eight-Core Summit Ridge Processor 3.0GHz Socket AM4 w/ Fan and Heatsink, Retail $294.49
https://www.superbiiz.com/detail.php?name=YD1600BOX&c=CJ
RAM
G.SKILL Ripjaws V Series 16GB (2 x 8GB) 288-Pin DDR4 SDRAM DDR4 3200 (PC4 25600) $119.99
DDR4 3200 (PC4 25600)
Timing 16-18-18-38
CAS Latency 16
Voltage 1.35V
https://www.newegg.com/Product/Product.aspx?Item=N82E16820232181
With a 1600 CPU, motherboard, and memory that will cost $399.97 without shipping and tax.
Video Card
$139.99
Sale Ends in 3 Days (Mon)
$129.99 after $10.00 rebate card
ASUS GeForce GTX 1050 Ti 4GB PHOENIX Fan Edition DVI-D HDMI DP 1.4 Gaming Graphics Card
4GB 128-Bit GDDR5
Core Clock 1290 MHz
Boost Clock 1392 MHz
1 x Native DVI-D 1 x Native HDMI 2.0b 1 x Native DisplayPort 1.4
768 CUDA Cores
PCI Express 3.0
https://www.newegg.com/Product/Product.aspx?Item=N82E16814126170&Tpk=N82E16814126170
With the above graphics card added $539.96 without shipping and tax. $15 in rebates makes it $524.96.
What is the power rating for your current power supply. That may need to be upgraded.
Start at 1:00 into the video for benchmarks.
Is a $160 CPU Enough for Gaming?
Tech YES City
Published on Jun 14, 2017
"Today we pit the AMD Ryzen 5 1400 against the Intel i7 7700k with the Radeon and Geforce Mid-Range Champions (The RX 580 & GTX 1060 Cards) to see how much of a difference there is and also whether the performance you could gain off a 7700k is worth it when compared to the Ryzen 5 1400. Everything in this comparison was overclocked to relatively normal levels for air and water overclocks."
https://www.youtube.com/watch?v=R173IbAXKX8
The Best $100 Entry-Level GPU? RX 560 vs. GTX 1050
Hardware Unboxed
Published on Jun 21, 2017
https://www.youtube.com/watch?v=lSURL-eC-SY
Edit: Power Supply
$54.99
Sale Ends in 5 Days (Wed)
Save: $15.00 (21%)
$34.99 after $20.00 rebate card
$2.99 Shipping (restrictions apply)
CORSAIR CX Series CX650 650W ATX12V 80 PLUS BRONZE Certified Active PFC Power Supply
https://www.newegg.com/Product/Product.aspx?Item=N82E16817139200