When I read about people benchmarking their systems with the screensaver glxgears, I always get a good laugh. The graphics are very simple, and use no advanced graphics techniques whatsoever. If you want to try this on your system just for kicks, run glxgears from the command line and a little window with gears in it will pop up. After a few seconds, it will start to display the frames per second on the command line. With the small window, my system averaged around 8,500 FPS. In the real world, you'll probably have full screen graphics applications. My system averaged 1,200 FPS in fullscreen mode. So, I see my system is super overkill for glxgears, and basically only gives me an idea that my openGL drivers are working as intended. So, how do we get a better idea of real world performance?
We need to install a program called Hardinfo. This program is in the Ubuntu repositories, and can easily be installed from the command line, or the package managers. Once installed, you'll find the program under system tools. Go ahead and open the program. The first thing you'll want to do is go to the information menu, and use the network updater. This will get benchmark results for other systems, and send results from your system. Then, from the information menu, select generate report, and then select everything (it should already be selected by default). Then just click the generate button, and it will start a series of tests. Try not to do anything while the tests are performed, or it may affect the results. Once its finished, it will ask you if you want to display the results in a browser. Tell it yes, and enjoy the results. Along with benchmarks, this is a great way to gather system data.
Hardinfo doesn't include any graphics tests. So, we're going to install something that can push our system and graphics card a little, unlike glxgears. There's a pretty cool open source game in the Ubuntu repositories called Nexuiz. After installing it, running the game and setting it up are a breeze. I turned all the graphics to maximum, with a 1280x1024 resolution. Then I changed anti-aliasing to 2x. There's also a setting in the menu to turn on the FPS display. Definitely do this. While running around fragging bots, I was trying to watch the FPS display as much as possible. I was getting somewhere around 40 FPS. This is a much more realistic test than the 1,200 FPS of glxgears. If you have commercial games that run in linux, they may be better to test actual performance, because they're probably much more optimized than the open source games.
After these simple tests, you should have a much better idea of how your system will perform in Ubuntu.