Need help for CPU and motherboard under 250 on Amazon

[ToxiicHydra]

So my parents let me upgrade my CPU and Motherboard but I don't know what CPU to buy. I really want a I5 because this pc is primarily for gaming. My budget is 250 bucks maybe 20 bucks over but nothing over that. This needs to include the motherboard aswell. I have a r9 380 and I want to play battlefield 4 and Smite on 60fps Ultra but high will be more than enough. I have'd planed to buy the AMD 8320 with a new motherboard is that good enough for these games?
I would preferably use a ATX board but mATX is okay.

 

[RazerZ]

What form factor do you need the motherboard to be? (Micro ATX, ATX, Mini ITX)

 

[RazerZ]

Is there any chance you can use sites besides amazon? With their pricing you will have to settle for a mATX board.

 

[NightAntilli]

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor ($175.88 @ OutletPC)
Motherboard: ASRock Z87 Extreme4 ATX LGA1150 Motherboard ($79.99 @ Newegg)
Total: $255.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-05 16:45 EDT-0400

 

[NightAntilli]

If you really want it from amazon, you're gonna have to give out a bit more money...

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor ($184.99 @ Amazon)
Motherboard: MSI H97 PC MATE ATX LGA1150 Motherboard ($89.99 @ Amazon)
Total: $274.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-07 16:13 EDT-0400