And I woudl like a brand new porsche 911 for $15k.
$300 does not even buy a basic computer to use for facebook and internet. Windows alone costs $85 so that leaves $215 for cpu, motherboard, ram, hard drive, case, power supply, and GPU. Your budget vs expectation is very very unreaslistic.
At $300 the best thing you can do is find a used gaming computer. Preferably with a core i3/i5 or fx-83xx processor.
And fyi that will be a 60hz setup and wont even be able to do 60fps.