I know its a bit over your budget but it would be worth it
Radeon RX 480 $229.99
Its not super high end or fancy but you will play everything including this game guaranteed. Its probably one of the best budget cards.
You can also try out:
GeForce GTX 1060 $199.99
GeForce GTX 960 $179.99
But I would not go any lower then that.
A geforce 950 would be around $150