I don't have very good knowledge of gaming requirements and stuff but I did my own research and this is what I am looking to buy. I would like to know if there is any problem with my pc and if it will run games like skyrim and bf3 on high-ultra settings. Thank you
That's very bad. Get a psu from a known good brand like Antec, Corsair, Seasonic, or XFX.
An HD 7870 should be sufficient to run Skyrim on Ultra and BF3 on High at 1920x1200, but Skyrim has better performance with Intel cpus (I don't remember whether BF3 also favors Intel cpus)
You dont need 800w. Go for a nice branded 600w, it's plenty. The whole PC would pull about 400w.
The issue with cheap PSUs is they are unreliable. They might have 12v rails that are over or under volt, they might fail hard and zap the GPU, they might not be able to even deliver the needed 400w for that computer.
A sufficiently bad psu can ruin all your other components, and the warranties probably won't cover that, so instead of saving $50, you're really gambling several hundred dollars that a no-name psu will have enough power and stay working until such time as you upgrade again or get rid of your computer for other reasons.
Where are you getting 495 watts? According to the eXtreme Power Supply Calculator Pro, that fx-6300 system with two 7870s (presuming you're getting one now and one later for crossfire) needs a minimum of 344 Watts (394 or more recommended) with 28.7 amps on the +12V rail. The Intel i3-3220 requires less than that.