An i7-3770 _should_ be on an Ivy Bridge motherboard, but could, theoretically, be on a Sandy Bridge board since they use the same LGA-1155 CPU socket. The standard Acer shipped with a Celeron CPU on a MB with an H61 chipset. Can you tell us what model MB you have, or at least what chipset is on the motherboard?
Since you are running a non-standard CPU, maybe your power supply isn't stock either - What kind of PSU do you have inside that thing?
What is your OS?
Is your computer set up to run on legacy BIOS or UEFI? When was your last BIOS update?
There is a reason the forum rules tell you to post your PC specs - it lets people know what they are actually working with, not guessing in the dark.
For your budget you could be looking at a lot of different cards. You might find a refurbished GTX 1080 for that price. But spending that money on a card that turns your system into a an expensive paperweight isn't going to do you any good.
Best case scenario - You have a Z77 chipset Ivy Bridge motherboard and the latest BIOS, running it with UEFI configured and you can stuff an RX 480 right in and power on and go.
Worst cast scenario - You have that stock H61 chipset MB, with legacy BIOS only, and the absolute best you can hope to run on the beast is about a GTX 600 or 700 series or an HD 6000/7000 or R7 300 series card depending on your BIOS and when it was last updated.