Yes, the 7750 is your best bet. But before buying, there is some things I'd like you, Kr4zyM3n4c3, to mull over.
Lets assume you decide to stick with your current system and upgrade it. You spend the money for whatever parts and you can play BF3 on low and are satisfied. A little bit of time passes and you start to get good at the game --by becoming a better player you start to notice inconsistencies in the game that are affecting your scores. These inconsistencies are little things such as a little stutter that seems to happen at the worst time, being killed for no apparent reason, and general lag. So you decide that your going to upgrade your CPU. Afterwards you think, "WOW, when I get in firefights there is no more stutter!" But you still seem to be dieing for no reason, like your missing out on some action. On VOIP people mention they know someone's coming because of shadows, and you notice your new CPU is only ever at 60% utilization in game.
You think to upgrade the video card again even after you just bought one not to long ago. Presently you may be thinking you won't, but at this time you may be hooked on the game, so you will. But before you even get to it your computer dies and it seems to be that the PSU failed from being overloaded. Your really pissed that you took that guy from the internet's advice on the 7750 and quad core CPU. So this time you get a really big and fast card with a 50 dollar PSU, the card doesn't fit properly due to the hard drive bays so you cut them out and set the hard drive in the spare cd drive's bay because it's the cheapest option.
This works and you play a few more months, one day while attempting to start a school report the PC refuses to power on. The newish PSU has also failed because a 500 watt power supply was used to power a card that lists the system requirement, "PSU with 500Watts minimum," this PSU with a price of only 50 bucks at that. And because you have a report due in a few days Good Ole' Murphy pays a visit, that PSU takes out your Hard Drive, new GPU, and motherboard.
You still have a newish AMD Quad Core plus a computer case. You have to rebuild the computer. Do you want to still go the cheap route with your existing poorly ventilated case and risk heat issues? Also the AMD chips is still good, but there's some much faster processors available, wanna go the cheap route?
At this point your pissed you spent a lot of money on that POS for nothing. Yet you have to spend more for an entirely new system you now realize you should have done in the first place.
Don't think this can happen? It most definitely can, because that scenario above was my (slightly altered to fit you better) experience, but include a cheap LCD monitor as well. I estimate I threw 1200 dollars out the window. What do I recommend you do? This:
1. Save up your money and get reputable, cooler, simpler, less gimmicky parts. Basically, avoid any part that "looks cool" with pretty colors, heat pipes everywhere, and fans everywhere.
2. Do not pay less than $100 dollars for a PSU. Look for a power supply that has a wattage of less than 6 times its retail price, that is the price before any special deals. Meaning a $100 PSU should not be expected to reliably give more than 600 watts of power. If you pay 100$ for a 750 watt PSU, and load it with 601watts for a few hours every day, I PROMISE you, it will fail before you were ready for it to go. I paid $160 for a 550Watt PSU 6 years ago and it is powering this vary PC. For a different, lower performance PC, I went through a 45$ 430 watt PSU, a 50$ 500 watt PSU, and a 70$ 600 watt PSU in 1.5 years. The current PSU for that system is a 450 Watt PSU that was $100. It's served 2 years now. Expensive PSU's are rated for the power they can reliably give continuously, cheap PSU's are rated for the power required to kill it.
3. Get near top tier now, parts that fall in the "performance" category, not the enthusiast category, not the value category. This will save you money in the end.
4. Get a SSD. Without one you will notice that your computer seems slow, performing at a crawl even though cpu usage is at 5%. This might prompt you to get one and spend a bunch of time reinstalling windows. You could get a transfer kit, but that another 20 bucks wasted, also a transferred installation will never perform like it could have.
5. Do it right the first time.
-DerekZ10