I would like it to be capable of running most modern games at higher end settings. If it could run something like Planet Side 2, or DOTA 2 at medium (if it bottlenecks from the CPU)/max settings (without bottlenecking) that would be fine.
I'm looking to add in a graphics card and upgrade the PSU. I would like to avoid touching the CPU or motherboard for the moment.
Currently I've been looking at this: http://www.newegg.com/Product/Product.aspx?Item=N82E168... as a graphics card, but I am unsure as to whether it would work with my current specs. Do I need to get a new motherboard/larger case? I've read some agreement that the 670 is worth the $100 higher price. Is that so?
I'm not really concerned with possible bottlenecking from my CPU unless it actually degrades performance, or breaks the computer. Upgrading the CPU is not in my budget at the moment, and even a bottlenecked GPU is better than integrated graphics. I will probably swap my i5 650 for this: http://www.newegg.com/Product/Product.aspx?Item=N82E168... at a later time.
I'd completely veto that power supply suggestion - that will not be able to work with a 660TI, you will need a 500W rated 80+ bronze minimum for that type of GPU. I will repeat every time: CHEAP POWER SUPPLIES ARE NOT WORTH IT. If you want a solid 500W I suggest this: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Before upgrading that build make sure the case can accommodate a large video card and full size power supply - not all proprietary cases will. Also 1156 sockets will not accept an i7-2600K, and that CPU isn't even worth it for gaming.
You might just want to do a whole new build - upgrading a PC like that will not really be worth it in the long run.