AE: Frame rate and animating solids
24 FPS should be plenty smooth, anything about 15fps should appear fairly smooth to the human eye.  There are two possibilities I can think of, first, you may be encoding to a fairly low compression format that produces large files, if so, your computer may be having trouble displaying the frames in time.  This can result in lag or frame skips which make the video look much less smooth.  

Second, you may need to apply some motion blur depending on the type of motion and objects you have.  While it makes the image less sharp, we naturally expect a certain amount of blur on things in motion and our brain sometimes things it is less smooth if there isn't a small amount of blur.  After Effects can render this, but it's not on by default as it adds additional render time.