if machine quilting, i just start with very small stitches, then onto 2.2 or 2.4 , then when done, i go back to very small stitches. i clip the thread ends.
if hand quilting, yes you can bury the threads.
i tend to trim my quilt top around but leave about 1/4 past the top edges. to fill the binding. i used 2 1/2 inch binding most times, or 2 1/4 inches.