You've come to the right place if you want help or upgrading your pc!
Definitely don't shell out all your money for a 570 because it would be bottlenecked by your cpu. Basically what bottlenecking is is when one piece of hardware simply cant perform as fast as another piece of hardware. If your cpu isn't fast enough to tell the gpu what to do then it will ultimately hold back your gpu and your gpu will not reach its full potential.
While I don't recommend going for such a high end gpu like a gtx 570 until you upgrade your cpu and psu you could definitely go for something a little more low end like a gts 450 http://www.newegg.com/Product/Product.aspx?Item=N82E16814127521 which still may be a little bit of overkill but if you decide to upgrade your system further you can still use it. Whatever you choose to upgrade to you will see a dramatic increase in performance in games because integrated graphics are not meant for games, they are meant for watching movies and displaying regular stuff on your screen.
Also, if you'd like a bigger case you could always for an antec 300 or something like that because they aren't terribly expensive and they'd give you room for an upgrade later on.
Hope this helps you reach a decision :)

Thank you so much for explaining to me what bottle necking is so now it looks like in order to pretty much reach some high fps I'm going to have to also upgrade the motherboard and CPU. Damn I didn't know my pc sucked so hard. Well thank you so much and ill keep saving in the meantime while some other suggestions show up as the more the merrier.

It's not so much the CPU itself, it's the low clock rate. If you are using the most recent BIOS, you could upgrade the CPU to a higher clock (2.8Ghz or above) Phenom II or Athlon II and be in the range you would need for a beefy graphics card.

First note, though, it that you will need to move up to a 400-500W PSU. A heavier CPU as well as a beefy GPU will absolutely smoke that 300W you have right now. Look for a PSU with active Power Factor Correction; they are a little more expensive, but with the potential draw a heavy GPU can cause, it assists in instability and random reboots or lockups.

What you really need is a new pc. Have you considered building you're own rig? You could build a very nice system with $600.

for 500-600 just build a new rig. If you want bang for the buck go with phenomx4 955 BE and pair it with a good motherboard, start from that and just balance everything out, like for ex. 40-80$ for SSD since you already have an extra hard disk, 60-80$ for a memory, 40-60$ for a computer case, a 100-150$ for a monitor and maybe 40-60$ for PSU. You may need to add a couple of bucks to get a decent video card since its the most essential part when were talking about gaming. I keep telling people don't ever hold back on the graphic card because most people use their pc for entertainment and your graphic card will help you get the most out of it. I have this uncle who always asks me to build him a pc but when we get to the graphic card part he skimps out and after that he would download(pirate) the most latest games and will ask me why is the graphics bad, I keep telling him for 8 years now and the mf still dont understand.

I opened an account here when saw a guy recommending a cheap power supply...that is the last place you want to go cheap. It gives the lifeblood of electricity to your computer... its very important.

i made a decent $800 build for you on newegg.com cause I'm bored.

800 dollar build for some guy

-AMD ASUS motherboard 970X = http://www.newegg.com/Product/Product.aspx?Item=N82E16813131757

-CORSAIR Professional Series Gold AX850 850W = http://www.newegg.com/Product/Product.aspx?Item=N82E16817139015

-2XG.SKILL Ripjaws Series 4GB 240-Pin DDR3 SDRAM DDR3 1600....two of these to start..http://www.newegg.com/Product/Product.aspx?Item=N82E16820231313

-COOLER MASTER GeminII S 120mm Sleeve CPU Cooler = http://www.newegg.com/Product/Product.aspx?Item=N82E16835103046

-SAPPHIRE 100315L Radeon HD 6850 1GB 256-bit GDDR5 <http://www.newegg.com/Product/Product.aspx?Item=N82E16814102908

-AMD Phenom II X4 955 Black Edition Deneb 3.2GHz < < fast processor so no bottle necks = http://www.newegg.com/Product/Product.aspx?Item=N82E16819103808

-COOLER MASTER HAF 912 << as the model name says high air flow and its cheap = http://www.newegg.com/Product/Product.aspx?Item=N82E16811119233

grand total up to this point is $754

add four 120mm case fans, take your pick

http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007998+600035590&QksAutoSuggestion=&ShowDeactivatedMark=False&Configurator=&IsNodeId=1&Subcategory=573&description=&Ntk=&CFG=&SpeTabStoreType=&AdvancedSearch=1&srchInDesc=

If you have that windows 7 disc this build just got easier...if not there goes another $100.

parts from the old computer you can salvage..
-640gb hard disc drive..i bet gateway put a Western Digital in there
-optical DVD/CD drive if it is a SATA interface
-fans?

And a monitor...i know its not a 19" but bigger is better..21.5" LED samsung = http://www.newegg.com/Product/Product.aspx?Item=N82E16824001484

Grand total with monitor is $950ish (note i didnt add any 120MM fans, thats up to you)

Upgrade path >>>
-another hard drive that is either a SSD (solid state disc) or a Western Digital Raptor
- AMDs Bulldozer 8 core processor when it comes out
-New mother board if you want to run crossfire or SLI or you could just get that to begin with..its up to you. A 990FX would be that upgrade = take your pick

http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007625+600008296+600166242&QksAutoSuggestion=&ShowDeactivatedMark=False&Configurator=&IsNodeId=1&Subcategory=22&description=&Ntk=&CFG=&SpeTabStoreType=&AdvancedSearch=1&srchInDesc=

I hope this helped

bobthenailer, hate to break it to you, but you have really over rated the PSU. Providing far too much wattage causes the PSU to recycle unused current through the inversion system, causing additional heat and load to the systems contained within the PSU, and will shorten the PSU's lifespan.

I am a freelance systems developer, and thoroughly educated on electrical principles, and tell you in detail that the habit of cramming HUGE power into a relatively simple machine is asking for failure.

More info here: http://www.3dgameman.com/forum/hardware/psu-advice#comment-1764900