Tmux expects you to rebind its leader to Ctrl-a once you're ready to move off of screen. Otherwise, it's default works nicely if you are nesting screen inside of Tmux or vis-versa
I use Ctrl-a as the "go back to beginning of line" shortcut that Readline-capable programs offer by default [1]. That's actually one reason I never got used to Screen ;)
[1] that is, using the Emacs keybindings it exposes by default. I know you can change that through .inputrc
