Check the cpu support list for your motherboard.
Likely, it will support a I7-4790K which should be well within your budget.
Likely, your motherboard will not support overclocking, but the I7-4790K runs at 4.0 stock with a higher turbo.
You may also want to buy a $35 cooler like the Cryorig H7.
A I5-4690K will cost some $100 less, but you would need to pay more than that for a overclocking capable motherboard.
How do I check the support list for my motherboard? It's a prebuilt PC and it doesn't say anything besides manufacturer name