The way you maintain a transparent background in Photoshop using alpha channels:
1. double click on your layer in the layer palette to unlock it
2. click the "channels" tab next to the layer tab
3. click on the "new channel" button at the bottom (this adds the alpha channel)
4. turn the eyeball on all the channel layers
5. do a "save as" and make sure the "alpha channels" button is checked
6. import into Final Cut Pro
It seems like there should be a more intuitive way to do this. I would love to hear if anyone has a simpler method.
Here's a frame grab of my alpha channel test. There is still a lot of green around the pigs, but I did not light this correctly. Once I shoot everything in the studio, there shouldn't be any green outline.

I also taught myself how to export flash movies with transparent backgrounds. To do this using Flash:
1. Have an animation ready and select "export" then "export movie"
2. Choose the save as a QuickTime format
3. Click Save
4. make sure the "Ignore stage color (generate alpha channel)" is checked
5. Click export
6. Import file into Final Cut Pro
Here's a test of this technique: