C-b is pretty bad for the same reason for users like me with with well-worn emacs key memory. I end up using the backtick, but it does make sharing a session that little bit more difficult.

I'm not sure about tmux, but you can still move to the beginning of the line by pressing C-a a in screen.

adding

  bind C-a send-prefix  

to your .tmux.conf file will allow you to type C-a twice and still get to the front of the line