Whilst i agree with above suggestions, the recommendations are blunt, i'll help refine.
I would personally use your $150 budget for a CPU upgrade but this will require a new Motherboard and RAM for a good upgrade and to a modern socket at that. Even a cheap Pentium G4560 will outperform the FX 6 Cores in games especially those that are single-thread intensive. Whilst you GPU isn't a super powerful card, it's modest and easily capable of running PUBG when paired with a more capable CPU. From your budget this seems like the best option:
PCPartPicker part list:
https://pcpartpicker.com/list/8TCHnn
Price breakdown by merchant: https://pcpartpicker.com/list/8TCHnn/by_merchant/
CPU: Intel - Pentium G4560 3.5GHz Dual-Core Processor ($58.88 @ OutletPC)
Motherboard: Gigabyte - GA-B250M-DS3H Micro ATX LGA1151 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill - Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory ($59.92 @ Amazon)
Total: $188.69
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-10 10:55 EDT-0400
It's slightly over budget but the best you can do with that much. It should help PUBG greatly and it is easily upgradable should you have more money later. You can always chuck in another 8GB kit of RAM for 16GB later and CPU can be swapped to an i5/i7 if you ever feel the want/need. With this, the build should be great for 1080p the settings i would recommend (even on a higher end system, i run the game at quite low settings simply because lack of optimisation and of course, competitive edge since grass and shadows only get in the way). Try > 100% Resolution scale, Ultra AA + PostFX but Very Low for everything else. Yes this won't look beautiful but should give you achievable FPS and i'm sure as a player you understand Very Low foliage, shadows and such only means it's easier to see enemy players. Should you get more money later, a new GPU wouldn't be so bad try save up for RX 570 4GB > RX 580 8GB > GTX 1070 > GTX 1080, etc. In order of cheaper/weaker to dearer/stronger. Hope this helps
See Pentium G4560 Benchmarks here *FX 6300 included* >
http://www.eurogamer.net/articles/digitalfoundry-2017-intel-pentium-g4560-budget-cpu-king-review