I sort of answered this
here, but I'll elaborate.
First off, don't edit at 60. It's not a standard mastering format, so your final video will eventually be converted to 24 or 30. Vimeo and Youtube will recognize that the video you're uploading is 60fps, and they'll automatically cut out every other frame to make it 30fps. If you make a DVD or BluRay, or any tape format, you have to convert it to 24 or 30fps too. So don't spend computing power while you're editing playing extra frames that will eventually get dropped, and personally I think you're better off seeing what the final frame rate will look like while you edit. Edit at whatever frame rate you plan on exporting.
Like the dude above me said, the choppy video is because you're only keeping 40% of the frames that you shot. If you export at 30fps, you'll keep 50% of the frames which will at least keep your motion smooth and constant.
Think of it like this. If you shoot 60 fps you end up with a simple frame order like this:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22...
Then you cut out 50% frames to go to 30fps, you still have a consistent pattern:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26...
But if you cut out 60% of the frames to go to 24fps, your pattern gets messed up.
2, 4, 7, 9, 12, 14, 17, 19, 24, 26, 29, 31, 34...
That's basically a mathematical representation of why your video looks jittery. A smooth shot doesn't skip frame 6 to jump from frame 4 to 7. There are fancy ways to blend your frames to make them look smooth (the poor man uses Twixtor, the rich guys use Terenex boxes) but none of them are simple or painless.
TL;DR - If you shoot at 60fps, edit at 30, and export at 30. If you want to export at 24, shoot at 24 or 48 and edit at 24.
