We do the semicircle motion here, too; and it's even "officially" called "The C for Ceroc" by many teachers.
I always use it to start, even though I've been dancing a while now. The primary reason is courtesy, as most of the ladies here have learned to follow the C as their lead-off, and I love partnering beginners and making them feel good about their dancing! So one of the alternative starts would be inappropriate in this situation.
However, all the teachers here discourage "bopping". Such behaviour includes: continually jiggling handholds in time to the beat (including repeatedly doing the "C"), constantly bobbing your head as you dance, marching with the feet instead of keeping them near the floor. These things make dancing a lot less stylish and reduce the clarity and quality of leads.