You need to about double your budget for a starter gaming laptop, something with a 950m video card. Even a gaming desktop would be double your budget, triple if you need a monitor, keyboard and mouse. Just the Windows OS is about $90.
You can get used business tower computer with an Intel i5 CPU with the OS license and a 300+ watt power supply, then get an nVidia GTX 750Ti video card to get a decent gaming computer for about $300.