The camera can shoot properly at these various frame rates - the file that it creates will always be 60i though. Here's how it works:
If you shoot at 60i it will take 60 pictures a second, throw out half of each frame (alternating even and odd lines) and save each frame as a single field in the final 60i signal.
If you shoot at 30p it will take 30 pictures per second, split each in half (even and odd lines) and save each half image as a field in the final 60i signal.
If you shoot at 24p it will take 24 pictures per second, split each in half (even and odd lines), then save the half frames as fields in an alternating pattern of 3 and 2 fields to produce the final 60i signal.
This last technique is called a 3/2 pulldown, and is the traditional way of converting footage shot on film at 24 frames per second to display it at the standard television rate of 60 fields per second. Most films that you've watched on television were probably encoded this way. It still will have a distinctly different and more "cinematic" look than stuff shot at 60i or 30p, so if that's your goal you definitely want to shoot at 24p.
For editing you have a couple of choices. The simplest is just to set your editor to treat the footage as 60i and edit away. This works, but can cause quality problems later if you output for the web - displaying interlaced footage on line doesn't work well (the problem you mentioned with visible jaggies) so you'll need to deinterlace the final output and that will drop the picture quality, as well as potentially creating odd movement in the footage because of the 3/2 sequencing of frames.
The second option is to do a 'reverse 3/2 pulldown' to extract the clean 24 frames from the 60i signal. You'll have to do this to all of your footage before you start editing - once you've edited each cut will change the timing on the 3/2 sequence so it can't be extracted cleanly at that point. Depending on the amount of footage you have this can take a lot of time to process and will take up more disc space because you need to make a copy of the footage once it's converted to 24p. You'll also need software designed to do this. After Effects does it well, but is expensive; JES Deinterlacer is a free option that works well but is mac-only - there is probably a windows-based equivalent but I don't know what it is. You don't want to just change the frame rate to 24 - that will throw out frames without regard for the 3/2 pattern and you'll get jerky motion in the final video.
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