Does Sony make AVCHD cameras? I thought that was a Panasonic format. I could be wrong though. All I've ever noticed were HDV, XDCam, from Sony consumer/prosumer HD.
 "I am a newbie, but aren't Sony DVCs not compatible with Final Cut Pro?"
I've never heard of anything not working in FCP from Sony. The only thing that may be buggy is HDV, but that's because it's HDV, not because it's Sony.
As mentioned earlier, RED one might give you problems, but I know that camera is made to be used with FCP. So you wouldn't have problems with that camera. I'm sure that camera is out of your price range and would be overkill for whatever you need though. Â