FPS Settings on a Comp

The frame rate of the footage determines the speed of the playback. If you shoot at 60fps and the footage is interpreted as 60 fps ten seconds of real-time will take ten seconds of screen time and all motion will look normal.

If you drop 60fps footage in a 30 fps comp 10 seconds of real-time in the footage will still be 10 seconds in the comp, you'll just see every other frame or blended frames, but the timing won't change. 10 seconds of 60 fps footage in a 10 fps comp or a 24 or 120 or even 999 fps comp would still take 10 seconds to playback. The only7 difference would be how many original frames would be dropped or blended per comp frame. 

If you need to change the playback speed of some footage you can change the frame rate interpretation of the footage using the project panel or the menu. This is the only time that changing the frame rate of a clip will not only change the duration of the clip, but it will change the pitch of the audio. 

I hope this helps. Unless you really want to have your comp run at 60fps, take a little more than twice the time to render, and realize that much of your potential audience will not be able to stream 60fps footage from YouTube or Vimeo anyway. If you like the feel of the motion at 24 and you want to include some 60 fps footage that plays back at the right speed then you don't have to change anything in the comp or footage settings, you only have to pock what frame blending mode you thing will give the best results. 

You may use the rd_compsetter script to set Comp Settings for a bunch of Comps (and preComps too) which is available for free (donations are welcomed) http://www.redefinery.com/ae/rd_scripts/

On your frame rate settings, it all depends on why you shot at 60fps and what are you intending to deliver, in terms of FPS.

If you want to deliver at 24fps, then you Interpret Footage accordingly and set Comp FPS accordingly; to 24 FPS.