Advice what video card to buy (better than my own, but not top level)

Hello, I bought a computer in 2010 HP, and it came with a video card ATI RADEON 4200 HD PCI-E
At that time, i did not have problem with it, since I was used to play an online game which did not use a lot of video potential.
But then my life got a little more busy, and i do not have the same time to play games anymore because works, college mainly, and others extra activities.

Because of that I bought battlefield 3 to play with my friends, and another game called Chivalry: Medieval Warfare.
I liked both games very much, except that I cannot play on full performance due my video card be very weak.

On battlefield 3 for example. I have set everything to the minimum possible, and i still get like only 15 FPS on clean maps, and like 8~12 fps on maps with more details, fogs, etc. I can't reduce anything more on graphics, and it really doesn't let me play well the game.

Then on Chivalry:Medieval warfare, I could do a lot more changing some stuff on the configuration files in the game folder to make it go lower than the in-game possible settings. The thing is, i can "play" the game, but it looks horrible. feels like I am playing a playstation game; and it is really sad since the game has awesome graphics. And again, even with decreasing all that graphic, i still don't get more than 20 fps...

I play also A.V.A fps game sometimes, and it is lower than all, and i still get max of 40 fps like..

So my question/advice is.
Which video card I could buy to improve my gaming?

Have in mind that first, I am very unable to spend money buying top cards right now, I want something in "between", better than what i got, but not something top lvl. I don't mind still playing those games on minimum settings(in-game without tweaks) as long as I can have a "playable" FPS on them.

I am asking this because right now I cannot spare a lot of money for this, i won't get in details, but right now all my money is being used for others expenses, so i have very little for myself right now.
I was thinking something between 50~100 usd only

My computer by the way before something ask is amd athlon II X2 255 Processor 3.10ghz
5gb ram.
I know it is not "top" configuration too, but i do believe that changing video card I would get the results I am seeking for right now, I say that because my friend's laptop for example has everything lower in config, but a better videocard, and the games there look way better and playable than on my computer.
I tried to overclock my videocard, but the stupid HP block a lot settings on my bios. I will never buy hp anymore i guess haha

So I would appreciate if you guys could give me a website to buy a videocard, or something, some opinions of a good card, that i can install myself etc.