OTHER RELEVANT SYSTEM SPECS: I have an HP Pavilion p6650z, 4GB DDR3 (Probably going to buy a 4GB stick as well)
MONITOR RESOLUTION: 1366x768
COMMENTS: I'm not worried about cooling, but I'm interested in getting a Geforce GTX 560 TI 2GB but I don't know much about how to find out if I can use it or not. I'm 90% sure it will fit in my case.
Any advice on getting this one or am I out of my league?
A GTX 560Ti is not recommend since a 300w PSU is too weak for that graphics card. At peak power it consumes 160w of power and I would not recommend anything less than a 450w good quality PSU for that graphics card (like Seasonic, Corsair, XFX, Enermax, PC Power & Cooling).
I recommend the Radeon HD 7750 which consumes a peak of 43w when playing a game. The resolution of the monitor is low so the Radeon HD 7750 should allow you to play games with high graphic settings, perhaps even ultra, with good performance. It will struggle with Metro 2033 and likely with Battlefield 3 as well with ultra graphics.