BaronKiller

Games will like GTA V will utilise those 4 threads and give a much better experience than a strictly 2-threaded Pentium.

I would go with the i3 because some games such as GTA require 4 core and the system would think you have 4 cores because you have 4 threads.

GTA and many other AAA games made after 2012 will outright refuse to run on a Pentium due to the dual cores.  The i3 would be best although I would perfer getting an i5 over an i3 and getting an SSD later.  The performance difference between an i3 and i5 is day and night.

about cpu            :             i3  6100   :  vs :   Pentium  : conclusion
Cores                  :                  2        : vs :   2             : both same 
threads                :                  4        : vs :   2             : i3 wins better performance in multitasking
hyper threading    :                 yes      : vs :   No           : i3 win HT is better than Non HT but still more cores is better than HT
Turbo boost         :                  No       : vs :  No            : both same
Clock speed        :            3.7 GHz     : vs :  3.3 GHz    : i3 win with more clock speed
If you are going to buy within this two cpu i3 is best no doubt.
 
Personal View : Normally games are GPU intensive like tom raider but some games are CPU intensive like GTA V so you will see good difference in FPS in those games. If you are dropping your idea to buy i5 for SSD than i will not recommend that idea because adding  a SSD is easier than replacing a CPU. with 4 cores i5 can easily beat i3 with hyper threading in multitasking and CPU intensive games. And turbo boost technology will help you in single task work, i5 6400 or i5 6500 is better choice than i3 6100.

But fps wont drop a lot will it and the 760 can still play BF4 at ultra at playable fps??

get the 8320 because the 8350 is only a oc version
and get any 990fx chipset motherboard
 
and yeah, the 8320 is more powerful than the i5

DDR3 2133(OC)/1866 is what it says, so probably not.
Why would you need 2400 anyways?

No. You can pair something as powerful as a 7950 before you'd get into any bottlenecking. 
In terms of value, the 750K is generally better and you should get it if it allows you to get better other parts or if you need to save money. It does the job quite well and I'd only recommend getting the 6300 if you had more money to spend. For gaming, the 750K/760K is great and you can use the extra money for a better gpu.

The 270 is a solid choice. Get the 7870 if it's cheaper.