Building/Buying a new pc?

[NightShift666]

Hello, I need help as I'm going to upgrade my PC as I can no longer stand having to play very few games on 20-15 FPS. So i'm stuck with two options. A)Sell my old computer and buy another one(Probably not because I'm on a tight budget and it took 2 years of good grades to make my parents even consider this) B) Upgrade my GPU or PSU. C) Upgrade the whole damn thing.

I need a good and cheap(Say under 120$, I'm not sure how many Egyptian pounds a dollar is.) GPU with a powersupply that is needed with it.
If I need to upgrade or buy, may someone please post a good hardware list that is also relatively cheap? I don't care if I can't run a specific game at max. I just want to have a good steady framerate at 1024X800 or slightly high resolutions. Even 600x400 can't cut it on most games.

My Specs:
Gigabyte GA-MA785G-UD3H
AMD Phenom X3 II 710(I trust this is a good one and I'm not sure I should upgrade this. Same for the ram.)
RAM: 3 GB DDR2
GPU: AMD radeon HD 4200(Now I'm sure this garbage is the entire reason my computer isn't able to run most games I present to it.)
PSU: 450W
Case: No idea, but it's a good one and my computer doesn't really overheat that much, even in 30+ C temperatures.
HDD: 320-350 GB, not sure exactly how much.

The games I want to be able to play:
Tribes ascend and blacklight retribution : Terrible 12-17 Frames per second, tried minicraft ini. and other tweaks, no difference. Almost unplayable.
Planetside 2: Obviously it's not released but I doubt I'd be able to play it.
Splinter cell conviction: Slow motion 20-25 Frames per second, not even a fraction of fun compared to playing on my brother's laptop.
FEAR 3, Borderlands, Assassins creed 2/Brotherhood/Revelations, Crysis 1 and 2, the mass effect series and sniper elite v2(And probably more I forgot about, I have a friend who gives me these games): Unplayable. Weather(I know this is probably a mistake to spell it like that) it's the screen tearing, slow motion that actually gives me a disadvantage rather than an advantage or Terrible mouse control due to the extremely low frames per second( last I checked it averaged 7). It's even more annoying when it's a mixture of all multiplied 10 times.

Also, If I need to buy another computer, can you please point out any universal brands such as Dell or HP that sell good PCs, regardless of stock or with upgrades?

I also have a question: What is needed for the GPU to function. I know the CPU needs a specific motherboard, does the GPU need that alongside a good Power supply?
I'm considering either the HD 3870 or the GTX 550 ti, as well as getting a 64 bit OS and upgrading my ram to 4-6 Gb.

I thank you in advance for the replies, don't hesitate to be honest with me.

A bit more information:
My CPU is clocked at 2.6 GHz and I'm not willing to overclock unless I'm desperate, and even the it'll be slightly.
I tried sereaching for good gaming builds that are cheap and one of them had the Athlon II X3 445 processor in the builds. I registered on the main site to check, it's 6 stars, like my current processor but will the 3.1 GHz make that much of a difference(24%?)?
I also tried comparing my current system to the system that I'm considering(same CPU, 3870 HD instead of current GPU, and 4GB), the current system has green or mostly yellow tick for all the games mentioned above in CPU and ram(Other than crysis and tribes for some reason) and a red cross on the GPU and overall on 1280
In the system I'm considering it gave yellow tick on cpu and ram and green in GPU on everything but crysis 1 and 2(All were green ticks).
Both were on 1280x1028 resolutions.
Will the 3870 be compatible with my CPU and motherboard(And no, my current computer isn't branded)
Also fun fact. My current GPU is always at least 150% weaker than the minimum.

[TherealYeno]

Your CPU isnt too bad so if you don;t have the budget you don't need to upgrade it now. If I were you I would never for such old cards like the 3870. I would get the 7750. With this card you won't have to change your PSU.