To check a GPU's compatibility, you need to check
- PSU
- Case
- CPU
For your case, I don't think the CPU should affect the GPU's performance since you are looking for a lower end card.
Check if a GPU can fit in your case and check if your power supply is strong enough to power the system with efficiency.
But like I said, all these factors aren't very important since you are looking for a lower end card.
for US$100 , the HD 7750 , R7 250 , and GTX 750 are some options you can choose from.