You can start with Adobe Premiere Pro/Adobe Creative Suite Production Premium. Register at Adobe to get a trial. Actually you might end liking it and using it since it offers full functionality for video creation/editing.
It's well optimized so should work smoothly unless you have a really terrible graphics card which I doubt. CS4 used to work on a Pentium 4 Desktop PC, CS5 needs a bit more since it requires the support for the newest technologies, shaders and Open GL but again I doubt that you'll have any problems running it.