I've used tmux on a daily basis for about four years and have no idea what -t or -s do. My workflow is from a single machine, where I don't need to have multiple sessions - just different windows. For any remote sessions, I just use screen. Doing so has the added benefit of not conflicting with others' workflows, which are likely screen-bound.

tmux's defaults are pretty much universally thought of as awful. Change ctrl-b fo ctrl-a and find some plugins that you like. Also, consider swapping Ctrl and capslock!

My conf: https://github.com/red-bin/dotfiles/blob/master/tmux.conf