Computer Upgrade

It should be fine size wise, and same with interface wise, the only thing it that the AMD website recommends a 400 watt or greater power supply. It SHOULDN'T need that as it does not require power cables (and therefore is limited to the 75 Watts that a PCIe slot provides) but it MAY need that depending on the power draw from your other components of your PC. I would look at a new power supply (400 Watts would be cheap, 50 bucks or less) and then buy the card. If the card works with no issues, don't bother getting a new power supply. If there is system instability, than get a new power supply.

Is there any reason you're buying a prebuilt computer over building it yourself? You could get a much powerful machine for the same price if you built your own.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Pentium G630 2.7GHz Dual-Core Processor ($61.77 @ NCIX US)
Motherboard: MSI H61M-P31 (G3) Micro ATX LGA1155 Motherboard ($39.00 @ Amazon)
Memory: Kingston HyperX Blu 8GB (2 x 4GB) DDR3-1333 Memory ($29.99 @ Newegg)
Storage: Hitachi Deskstar 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ Newegg)
Video Card: EVGA GeForce GTX 650 Ti 1GB Video Card ($139.99 @ Amazon)
Case: Rosewill REDBONE ATX Mid Tower Case ($34.99 @ Newegg)
Power Supply: Antec 450W ATX12V Power Supply ($31.64 @ NCIX US)
Operating System: Microsoft Windows 7 Home Premium SP1 (64-bit) ($91.99 @ Amazon)
Total: $489.36
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2012-11-12 07:39 EST-0500)

Unfortunately, this economy sucks for me, and im not looking for high graphics, so the budget is extreme low at around $300. So a build-your-own beast computer is out-of-reach. So i looked into other options. Thanks though.

So it will fit for sure? That was my greatest worry. Now if i did need a 400 watt power supply, what kind of system instability are we talking about? and if i just bought the power supply and didn't need it would it jack up my computer? Oh the questions, thanks for the help though.

Well, you linked a PC for $370 and a graphics card for $115, in total it would cost you $485, so I targeted that budget with my build.

I can make a cheaper build, too. Plus, you won't need to worry about a power supply unit failing on you or whether the graphics card will fit.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Celeron G540 2.5GHz Dual-Core Processor ($44.99 @ Amazon)
Motherboard: MSI H61M-P31 (G3) Micro ATX LGA1155 Motherboard ($39.00 @ Amazon)
Memory: Pareema 4GB (2 x 2GB) DDR3-1333 Memory ($18.99 @ Newegg)
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($52.99 @ NCIX US)
Video Card: Gigabyte Radeon HD 7770 1GB Video Card ($115.50 @ NCIX US)
Case: Rosewill REDBONE ATX Mid Tower Case ($34.99 @ Newegg)
Power Supply: Antec 350W ATX12V Power Supply ($23.17 @ NCIX US)
Operating System: Microsoft Windows 7 Home Premium SP1 (64-bit) ($91.99 @ Amazon)
Total: $421.62
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2012-11-12 09:05 EST-0500)

Not only it will be $65 cheaper, but it will also be faster.

Hahaha you're right, but the computer is at the peak of price for my parents and i plan on buying the graphics card with Christmas money from my grandparents. I should have mentioned that earlier. And i really dont want to jump right into building one with absolutely no experience. I realize there are a bunch of guides but i'd like to take this one slowly. Thanks though! ANd is one a 1-gig graphics card actually any good? Id really like to consider building, but my parents are sort of against it overall. ALthough it would be cheaper.

The only way to get experience is to build it yourself  . Just watch this video, and you'll realize how easy it is:

http://www.youtube.com/watch?v=d_56kyib-Ls

I understand it may seem to be rocket science at first, but it really isn't. And you could just buy the PC without the graphics card first as well - it will work just fine.

You know, i really, honestly appreciate tthe help and i will definitely refer back to this when i get to building my own. But in all reality, i will most be playing multiplayer games, be it fps or rpg like gw2 or blops 2. Im not quite going for high end yet. As long as it will play my multiplayer games, im all good for now.

It's far from high end  . And trust me, it will save you headaches associated with pre built machines. I know I might sound annoying, but trust me, this is the way to buy computers, be it low budget or high, suited for watching movies or gaming, done by a 15 year old or an 80 year old.

Start with a quad core processor and a board that supports pci16X.
The board should NOT have built in graphics.
If you are using dual core CPU, you are wasting your money.
The trouble with so many builds is that there are not enough resources and CPU to support good graphics...biggest mistake made.
Spend more, and get what you really want.

WRONG: do not put your OS on a 1 TB drive.
Use a separate drive for the OS which is SMALL and FAST.
A 1 TB drive will slow your system down, to a crawl.

No offense, but please understand that the higher capacity a hard drive is, the higher data density, which means higher read speeds  .

Also try to understand i have little understanding of what you just said.   Im that person right now, i don't wish to be, but i happen to.