You'll struggle massively with such a low budget.
Latest games require new tech, and don't tend ti scale down well to older hardware.
Maybe the second hand market is best, might pick up an AMD 5650 or 5750 for around that price. Probably a big ask though.
Find $100 and your in a better position, as buying a cheaper card now will mean as soon as tech moves on you'll be in the same position as you are now.