New gaming PC

[farisibakir]

Hi, I want to upgrade my computer for gaming.
I want to play games like BF4 , PES 14 , Minecraft , Crysis 3 , GTA V on medium setting with no lag.
I only need help with the CPU and the MOTHERBOARD.
Not with the old graphic card,ram,display,mouse,cooler,keyboard...
These are my current spec:
Video Card:ATI Radeon HD 5770
RAM:2x4GB 1600MHz
OS:Windows 8
Hard Disk:250 GB
I am from Bosnia so I dont have a lot of options.
My budget is very low and I dont buy online.
These are the CPUs I have available:
FX-6300
CORE i3-4330
CORE i3-4130
CORE i3-3250
CORE i3-3245
A8-6600K
FX-4300
A10-5800K
Athlon II 750K
A8-5600K
CORE i3-3240
CORE i3-3220
FX-4130
A8-5500
FX-4100
Athlon II 740
CORE i3-3210
A8-3870K
PENTIUM G3420
CORE i3-2100
PENTIUM G3220

The prize range for the CPU is lower then these processor.
I want you to choose the best processor from the list, and a new motherboard for that CPU.
Motherboard should be the cheapest to support 4xDDR-1600.(I think it is the only important thing)
Is the motherboard important??
I didnt buy anything yet because I am waiting for someones detailed explanation.
I am quite new at this, but I have did a lot of research and I think the best combination is:
CPU:AMD FX-6300
MOTHERBOARD:GIGABYTE MB GA-970A-DS3

I already have the HD 5770 so I am not changing it any time soon.
Just tell me whats the best processor on the list, and a cheap motherboard for it?
I already posted thousand times so I REALLY NEED YOUR HELP!!!

 

[GhostRyder]

Heres the issue, an HD 5770 is very dated at this point and will hinder you the most in gaming. Its passmark score is only 1600 which is very low by todays standards and wont let you play BF4 on Medium except at a resolution lower than 1080p.

With your selection of CPU's I would get the FX 6300 as that's going to be you best bet honestly from the list you provided. With your motherboard selection, that should be more than fine as well, though I normally would shoot for a 990FX chipset if you could.