FCP7 is (generally speaking) directly compatible with any camcorder recording in the AVCHD format, but only when set to record in 1080i60, 1080p29.97, 1080p23.98 or 720p. It is not compatible with AVCHD material recorded in AVCHD 1080p60 - the format was not standardized when Apple abandoned FCP7.
You ingest the material from the camera media via Log and Transfer, not Log and Capture.
For other tapeless formats, or for ingesting AVCHD 1080p60, you can use a third party convertor such as Edit Ready:
http://www.divergentmedia.com/editready
which will convert the material to Pro Res and you can directly import, and work with, Pro Res files in FCP-7.
You might want to view this tutorial about the tapeless workflow from frequent forum contributor Shane Ross:
https://www.youtube.com/watch?v=AhDnyWFAM10
It is hard to recommend any small camcorder, even though the picture quality is really quite good, I find the small viewfinders very difficult to work with. Is is such a subjective thing that you really need to hold it in your hand and shoot some footage to see if you can live with the camera or not.
MtD