Here's my build and why I would do it.
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 7 1700 3.0GHz 8-Core Processor ($289.88 @ OutletPC)
Motherboard: ASRock - AB350 Pro4 ATX AM4 Motherboard ($81.98 @ Newegg)
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3000 Memory ($124.99 @ Newegg)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($46.88 @ OutletPC)
Video Card: EVGA - GeForce GTX 1070 8GB SC Gaming ACX 3.0 Video Card ($454.98 @ Newegg)
Case: Zalman - Z1 ATX Mid Tower Case ($38.99 @ SuperBiiz)
Power Supply: EVGA - SuperNOVA G3 650W 80+ Gold Certified Fully-Modular ATX Power Supply ($99.99 @ Amazon)
Total: $1137.69
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-08-06 02:19 EDT-0400
First off, the CPU. Ryzen 7 has slightly better Single Core performance over Ryzen 5, and PUBG loves Single Core. Because the ARMA Engine is bad at Multi-threading, IDK why it's not on something like Unreal 4 or something more Multi-Thread capable, but... Meh. Next you might be miffed to see no CPU Cooler. The Wraith RGB cooler is actually a really good cooler and can get a R7 1700 to about 3.7Ghz on average before it starts getting too hot. And, it's RGB enabled, not that you would see it in the case that I picked.
Next, the Motherboard. B350 is an awesome chipset. It's cheap, allows for Overclocking, and just works. No need for those fancy X370 chipsets unless you are doing Multi-GPU or have a bucketload of M.2 storage, which you will have none with this build.
Memory is up next to the chopping block. Ryzen loves fast RAM, so I had to build around that constraint, and that 3000 speed kit will work beautifully for Ryzen.
Storage... I picked an HDD because I didn't know if you were willing to salvage an HDD from a prior build or something like that. So, I just threw it in there and forgoed an SSD because while nice, they are still a luxury.
GPU was a no-brainer. The 1070 is a solid GPU, and Vega benchmarks aren't out, but I doubt that Vega 56 will be fast enough on a Stock Cooler to be able to stay cold AND have good 1080p and 1440p performance. AND Since PUBG is still on DX11, you will still have good DX11 and DX9 performance due to Nvidia still heavily supporting those API's. DX12 and Vulkan performance will suffer a bit, but not by much.
Case and PSU are the finale to this great build. I picked the cheapest case with good airflow. It's no-frills, it just works. If you want something with a Window... The Zalman Z3 Plus is only 10 bucks more to show off your Wraith RGB bling. PSU, I honestly really only trust OEM's and EVGA PSU's. I love my EVGA G2 Supernova 650. And I'll pick up a G3 Supernova 750 for my next PSU so that if I want to go Vega 64 or larger, I'll have enough wattage to OC + use the parts.
Also, as an added bonus, this PC would do well with Streaming! Ryzen 7 is a great H.264 Encoding CPU with it being a cheap 8C/16T option for new streamers at about 300 USD.