Sam Hain :
https://www.youtube.com/watch?v=qWz7uipF9Ks This may be as "good" as it gets for your budget, otherwise... Keep saving and adding to your budget throughout the year for a better option(s).
Problems with that....prices almost all the components used are much more now especially GPU's.
lets look at individual cost
G4560 $55 used
Motherboard $50 used
RAM 8GB DDR4 $88
GPU decent enough to handle PUPG with more than 2GB of VRAM Atleast $80
...................
Your now out of Budget
You may be able to find a old Dell or HP business machine for around $150 with either a i5-2400 or LGA1366 Xeon and then drop another $120 for a RX 460 or 1050 GT.