Sony cameras usually work well with iMovie, and a lot of people use them.
Some Sony cameras shoot both AVCHD and standard def MPEG2. If you have both on your card, it may be necessary to import the MPEG2 first, then delete it and import the AVCHD. Check the manual to be sure.
Also, these cards are formatted as FAT32 which tends to get fragmented over time, so it is good to reformat it (or initialize it) through your camera's menu from time to time. Do not reformat it until you have saved everything on the card because this will erase it.
Also, see this article. Make sure you are on at least OSX 10.6.7, and better yet, be on Mountain Lion (10.8.3).
http://support.apple.com/kb/TS3720
Also, I found this on the Sony site.
http://support.d-imaging.sony.co.jp/imsoft/Mac/import/us.html