Mp4 is pretty universal, so if that is what is working in FCP, I would stick
with that.
Here's a link that lists the formats supported by FCP"
https://support.apple.com/kb/PH12754?locale=en_US
As you can see from the above link, Mp4 is one of the container formats
supported.
If you still have iMovie 6 on your computer you can share out your projects as movies, and import those into Final Cut Pro. Or, you can control-click on the iMovie 6 project's icon and select and click on Show Package Contents. You then will see a screen something like this:

The media for the project will be in the Media folder. You can Option-drag (copy, not move) the media to your desktop and from there import into iMovie 10 or Final Cut Pro.
Also, if by chance you have iMovie 8 or 9 on your computer I believe that you can update your iMovie 6 projects into it, and from there update the projects and events into iMovie 10. I have read this but not tried it myself.
-- Rich