I wouldn't plug either of those cards into that PSU, it's just not enough power. As to which card is better, I will share with you what I share with so many other people, on of my most favorite places to START looking at which of two cards is better.
Unless you run multiple monitors, HD 7850 is far more than enough for you. Save the money for some future upgrades.7950 and 7870 are high end cards. maybe your processor can't handle them. Also the PSU. Please check the compatibility of even hd 7850 before buying them. To tell you the truth, core i3 performs better than A6-3650 in games. So if you are getting a new rig very soon, then buy the 7870. I think it has better price to performance ratio
The most future-proof components you can put in your system are your case and your power supply.
It never hurts to spend extra money on your power supply. It might seem like a lousy use of your money, but your future self will thank you if you get a better one now. A weak/"just-good-enough" power supply will either limit your upgrade options (as you're seeing now) and/or will die and fry things in your system when it does.
Those should work well together and I can SLI in the future if I need to... right?
And what can I expect from that card? I'm hoping to max out games like: Fallout series, Left 4 Dead series, Call of Duty series, NBA 2k series. And I want to play games like Crysis and BF3 on, at least, medium settings. Resolution of 1920x1080.
Yeah, you should meet that for all of those games, at about 30-60 fps, sometimes more or less, point being you will be able to play games with that card, you will just have to play around with setting until you get the performance you want, but bf3 is really demanding in multiplayer, so you will have to play with settings especially for that game, good luck man, and you may be able to sli with that psu, but you should post info on your motherboard so we can know for sure
That's actually a little bit on the expensive side for a 560, granted it's a higher end company and has two fans in it. But like always $20 would be able to get you a card a step above that, in this case a 560Ti, a very well spent extra $20 or in this case $30 actually.
I'm pretty sure ZOTAC isn't a no name manufacturer. I've used two (9800GTX+, and GTS 450) and seen them in several high end builds. I've never really heard anything negative, so while it might not quite be an EVGA card, it's still pretty damn good. Feel free to chime in if I'm wrong.