Best driver for ATI Radeon HD4250
Solution 1:
In many cases using the proprietary ATI provides better performance, if your graphics card is supported you should be able to select it from the "Additional Drivers" application.
Solution 2:
I've been using ubuntu as my main OS for some years with AMD Radeon, what I can tell you is that the open source drivers work pretty well but I still prefere the Propietary ones.
For installing the propietary drivers you have to make sure to uninstall and completely remove the open source ones (from system configurarion -> aditional drivers, uncheck them if active and then restart)
Download the propietary driver from here http://support.amd.com/us/gpudownload/Pages/index.aspx
And just open the terminal and type
Sudo sh
Drag the downloaded (*.run) file and press enter (dragging a file to the terminal makes it easier to get the path of the file instead of type it manually)
The idea is to get something like this
Sudo sh 'path/to/your/file.run'
When the installatuion is complete type
Sudo aticonfig --initial -f
If later on you want to uninstall type this
Sudo sh aticonfig --uninstall
Restart and your are good to go, also you can install Ccsm or Compiz config settings manager from the Ubuntu Software Center to make what TK Kocheran says, that makes a huge difference