Do you have any parts already like monitor and such? You won't get much gaming computer for less than $300. A good gaming CPU alone would be close to $200 and a capable GPU would be at least somewhat $250. On top of that you will need to add Motherboard, DDR4 RAM, PSU, Case, Storage and maybe monitor and peripherals.
You need to remember that a computer needs a lot higher specs to perform equal to a console, as console games are very optimized for the specific hardware in the console.