This is the prime purpose of Final Cut. You really need to learn to use it as this is exacly what it was designed for. There is no need to trim the video first with QT. Just keep it all in one but folder Final Cut can pull what it needs from the larger untrimmed files
After spending the $$ on Final Cut Express you really should spend the time to learn how to use it. One of the best ways to learn is to watch a few video tutorials. These guys have some good ones. You can either buy the viedo or buy a subscription and then watch as many as you like. There are some free excerts so you can see what the quality is like before you buy.
http://www.macprovideo.com/tutorials/finalcutpro