I have a Github dotfiles repo so I can set it up on any server in a couple of minutes, just by cloning the repo and running a script within it. If you're jumping between different servers, I would highly recommend having a quick way to setup config like this. It's a short investment that pays dividends for many years - not just for tmux config, but setup for bash, vim, and any other utils you rely on.
I use one tmux prefix for the local machine and another one for ssh sessions (setup in bash_profile using something like `if [[ -n "$SSH_CLIENT" ]] ; then tmux set-prefix ... etc`. You need different prefixes when using tmux recursively like this, so you can navigate both the inner and outer session.
I also use a different color theme for ssh sessions, whch helps to know which prefix to use until it becomes somewhat subconscious.