There are many full-screen text editors, but if you want to edit files locally on your Mac and ssh'd while on a remote server without thinking about it, you really need to study one of the ubiquitous editors.
In fact, ideally, you should learn the basics of all three — at least how to exit safely — because at some point you accidentally make a mistake when you see that VISUAL is disabled or not installed correctly, and you will end up in the wrong editor.
nano (and his relatives in the pico family) is by far the easiest way to find out if you are coming from a TextEdit / TeachText / Notepad background. However, he is the least ubiquitous, and least effective with both keystrokes and screen real estate, and real Unix riders will laugh at you if they ask for “vi or emacs” and you say “nano”.
vi (and its relatives - in fact, usually you use vim, not vi) is the most common and certainly the most effective for quick and easy changes. It is also much more useful for fancy terminals such as your favorite iPad ssh client (where ^ X is the main task). And ultimately, most vi keys also work with ed, and sometimes even sed, which is great when you're stuck on a terminal with full-screen support in general. However, it is much more difficult to find out when you start from the background of the graphical interface - the idea that you cannot enter or edit text in a text editor, except to enter special modes, is just strange.
emacs (and its relatives and simplified clones like jove and ue) are the most efficient for performing complex operations. It's also nice that its weirder keystrokes (like ^ AF for moving the cursor) are the same as the terminal's command line, libreadline, Mac's built-in textual controls and Firefox text controls. And if you are really learning emacs, you can start using Aquamacs in the GUI and program it to automate all your tedious text editing, etc. The only problem is that actually learning emacs will take you years and you may have other things related to your life.