The only real downsites are if you use screen/minicom/etc inside tmux you tend to mash Ctrl-a quite a lot, but if anything that's easier than keeping track of which key goes with which level?

The above is how most people first configure tmux, since C-b is just awkward. `bind-key C-a send-prefix` is optional of course, but is used to forward C-a to the active window (beginning-of-line in shell and emacs). How would you do that in screen?

The default for `previous-window` is `prefix-p`. Run `tmux list-keys` to see all active bindings.