The easiest build you could do that cheap for gaming is a dell or some old office pc (with at least a 4 thread semi modern cpu and 8 gigs of ram) and a low power RX 460/560/1050 that dosn't need any external power, or a 1050 ti if you can stretch your budget a bit, but a used RX 460 2 gb is only 100 dollars and can run most modern games 1080p low settings 30 fps. But honestly, even if you find a 1050/460 or whatever that needs a 6 pin, the cards are only rates for slightly above or exactly 75 watts so you could probably get away with a molex to 6 pin only becauae the cards can get 90 percent of the power from the morherboard.
You could also build using used parts
35- Cheap mid atx tower case
45-Cheap name brand power supply
45-500 gig ssd
100-Used RX 460 2 gb
That leaves less than 100 for cpu/Mobo/ram, you might end up spending closer to 350/400 if you want a decent older i5 quad core and 8 gigs of ram, if you stretched your budget to 500ish you could get a gtx 1050 ti, a used nice i5/i7 with 8 gigs ddr3.
Normally I also recommend a hard drive for storage, but hard drives under 1 terbyte arnt really cheaper than ssds so you might as well just get an SSD.