Need Help upgrading some PC parts

[SageHasGame]

I built my PC around 5 years ago and want to upgrade some of the parts. My main goal is to play games smoother than I am able to right now.
I mostly play games like H1Z1/Battlefield, which requires a good CPU but I am also looking to upgrade my graphics card.

Recommended Requirements for H1:
Processor: Intel i5 Quad Core or higher / AMD Phenom II X6 or higher
Graphics: nVidia GeForce GTX 560 series or higher / AMD HD 6870 or higher

Recommended Requirements for BF1:
Processor (Intel): Core i5 6600K
Graphics: AMD Radeon HD 7850 2GB / Graphics card (Nvidia): Nvidia GeForce GTX 660 2GB

My current setup:
Processor: Intel Core i3-3220 @ 3.30GHz
Graphics: AMD Radeon R9 200 Series (not exactly sure which one but not high end)
Motherboard (to make sure it fits): https://us.msi.com/Motherboard/B75MA-E33.html#hero-overview
RAM: 8 GB

My ultimate goal is to get smooth FPS around the 100s, preferably 140 because of my monitor. I am willing to spend AROUND $500 and the products need to be from Amazon.

 

[chassmith]

just putting it out there

http://gpushack.com/collections/all-gpus-for-sale/products/msi-gtx-960-100me

if i had the money it would be mine right now.
when i do my next UP it is coming from them as there prices are crazy guud

I am sure poping in an I-5 and getting a good video card would do you wonders
I am an amd guy myself so no clue with I-5 to get with your mobo yahda yah da

 

[Autocrat]

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor ($240.00 @ Amazon)
Video Card: EVGA GeForce GTX 1060 6GB 6GB SC GAMING Video Card ($289.00 @ Amazon)
Total: $529.00
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-10-31 19:12 EDT-0400


I don't really know if it is worth throwing $500 into a 1155 mobo.

 

[SageHasGame]

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor ($240.00 @ Amazon)
Video Card: EVGA GeForce GTX 1060 6GB 6GB SC GAMING Video Card ($289.00 @ Amazon)
Total: $529.00
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-10-31 19:12 EDT-0400


I don't really know if it is worth throwing $500 into a 1155 mobo.

So if it's not really worth to throw in $500, what would be a better option? I'm obviously willing to pay less as long as it suffices for at least 4 years or so.