Your CPU is a major bottleneck in some of the titles which you desire to play.
i5 650 < i3 2100 It might be surprising to you how an i5 is slower than an i3 but in that generation, the i5 650 was a
dual-core hyper-threaded CPU, not a quad-core.
Now look at where the faster i3-2100 ends up -- especially the minimums are poor.
I would NOT go with an AMD GPU for your dual-core processor. Here is an example of why based on one game you mentioned:
I would probably buy a
$145 950 or a
$160 960 and after scrap your entire rig and do a DIY build once you save up $.
Don't bother upgrading the PSU as your CPU+950/960 won't even touch 200W of total power. This is the total system power usage with a
130W TDP 5960X and a GTX950/960:
You can buy a new PSU in 2-3 years when you decide to do a complete system overhaul. Right now your CPU is such a huge anchor that anything above a 950/960 will be wasted in many games so there is no point wasting extra $ on your outdated rig.
You are in a tough position because BF multi-player is also very CPU intensive. So no matter what $100+ GPU you buy, you'll be CPU limited in some areas where the game engine/AI hammers the dual-core CPU and minimums plummet.