After this lecture, you should go through vimtutor and/or the emacs tutorial
Some differences between the text editors:
Both vim and emacs are very powerful, so you should learn to use one of those if you plan on editing text a lot (ie, for programming). Other editors like nano have a lower learning curve, but fewer advanced features.
Emacs has more features bulit in than Vim. Vim's philosophy is to do one thing and one thing well, so it doesn't strive to have as many features built in as Emacs. You can install plugins to either to give them pretty much any feature since both have large communities.
Emacs is bigger than Vim, but that probably doesn't matter.
Vim or vi will be installed on almost every unix machine in the universe, whereas emacs sometimes won't be installed by default. This probably won't matter either.
Vim has a higher learning curve than emacs because it's a modal editor, but that also means that most things require less typing in vim than in emacs (you may hear about an "emacs pinky" where emacs typists have to hit ctrl so much that their pinky becomes sore; if you use emacs, you should probably rebind ctrl to caps lock)