The i3-2120 is likely to be a bottleneck to the system if you were to only upgrade your graphics card to a GTX 970. The i3-2120 is only a dual-core CPU (with 4 threads), while the i5-3470 is quad-core; many modern games benefit from multiple CPU cores (and some even require a four-core CPU, such as Fallout 4).
The i5-3470 is much more efficient and newer than the i3-2120 (with a newer manufacturing process).
It really depends on what games you plan on playing with your upgrade, for example Grand Theft Auto V will benefit from the i5-3470's performance, far more than a game focusing on graphical elements will.
For Star Citizen I, its system requirements seem to focus on the CPU rather than the GPU, therefore you'd definitely be better-off with the i5-3470 & the 960.
Your motherboard has three PCI-E slots, so you might benefit in using both the 960 & 550Ti, with the 550Ti dedicated to PhysX. The amount of RAM you have is fine for gaming.
If you do not mind purchasing used parts, I'd recommend you get a 290X (eBay has tons of them) as you get more graphical power for less (in the UK, used 290X GPUs sell for around £160 while new 970s sell for around £200, making a used 290X £40 cheaper).
Ensure your power-supply is able to power a 290X- you should have at least a 550W PSU, with the recommended wattage being 600W. Bear in mind that if you do go down this route you won't be able to support the 290X with your current 550Ti.
You might also be able to get the i5-3470 (or an even better CPU) used as well, along with the 290X. It really depends how much you're willing to spend on upgrading.