I can't find if this motherboard has a PCI-e 16x times slot or not. The specs don't mention the expansion cards.
I doubt you will be able to find a CPU much more powerful that would work with that computer. Even though the chipset does support up to core 2 duo, you'd need to find out the bios support from eMachines. Besides, the E5400 should be sufficient for your needs if you are on a budget.
You didn't mention an exact price but here are my suggestions. The PSU is the same for each but each GPU will not be significantly held back by your CPU in most games. The GPUs are each, in my opinion, the best in their pricerange. Don't forget, you need a PCI-e 16x slot in your motherboard for any of them to work. If you intend to spend more on the video card, then I have suggestions but it would require a better power supply than the one I am about to suggest.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371034
The radeon 4650 - the minimum. This is the minimum card you should get for gaming. The difference will be night and day between this card and the integrated you already have. Expect to play less demanding games at lowered settings.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150393
Radeon 4670 - worth the price hike but there are much better cards for only a minor price increase. It's performance approaches the radeon 3870.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150450
Radeon 5670 - for less than $100 you have a DX11 capable GPU that surpasses the performance of the radeon 3870.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150466
For comparison purposes, with my radeon 3870, I can play most games at 1920x1080 at either very high or high settings at 60+ FPS. I have an Athlon IIx4 at 3.25GHz. I can play crysis on medium at 30FPS. Cryostasis is all buy beyond me. Comparatively, your CPU is about equal to an Athlon IIx2 at 2.9-3.0GHz. This will not be significant with any of the cards I mentioned except in a few more CPU dependent games like Dragon Age.
Let me know your exact budget if it is more and I will post another comment with revised suggestions.