What is a good CPU upgrade from i3 3220 for a GTX 960?

[based_tobeh]

Hello. So, i'm planning on upgrading my 2-3 years old i3 3220 to a better CPU because i noticed fps drop on some CPU intensive game. Let's just go straight to the question and details.

What is a good CPU upgrade from i3 3220 for a GTX 960?

I have a 550W PSU and my motherboard is Gigabyte B75M-HD3 (LGA 1155).
If there's no LGA 1155 CPU worth upgrading to, i won't mind changing my motherboard.

My budget is around ~200$ for the CPU and ~100$ for the motherboard (if i had to change my motherboard).

Notes:
- I'm looking for a cool CPU.
- I'm not planning to do a hardcore (lol) overclocking on my CPU. Unless the temp is low, i'll do it.

Sorry for my bad english.
Thanks !

 

[turkey3_scratch]

Hop on the whole upgrade train here! A lot of people will just recommend upgrading to another Ivy bridge CPU, but I disagree. With you budget you can easily go Skylake.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($199.89 @ OutletPC)
Motherboard: Gigabyte GA-H110M-A Micro ATX LGA1151 Motherboard ($49.99 @ Amazon)
Memory: Corsair Vengeance LPX 8GB (2 x 4GB) DDR4-2133 Memory ($45.99 @ Amazon)
Total: $295.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-03-05 11:04 EST-0500

 

[Karsten75]

The Turkey_dude is correct.Unless you can find an i5 processor in LGA 1155 (Sandy Bridge) format for substantially less than these listed proces (http://pcpartpicker.com/parts/cpu/#k=14&s=12&sort=a7&page=1), upgrade to Ivy Bridge and 'git 'er done.