Now, these are huge files, so my use case is pushing it, but you'll want to be able to use and modify your lecture notes for years, so I'd suggest something lighter weight like a plain markdown file.
Whatever you do, take care of version control and backup.
I assume the things you'll want to track are facts and tasks. You'll want to capture as quickly as possible for later organization.
It really is as simple as typing to get started. Then you can go back later and re-organize your notes, tasks, etc. according to whichever system you prefer.
Some tutorials that seem to be well-paced for org newbies are available at http://orgmode.org/worg/org-tutorials/.
http://sachachua.com/blog/2008/01/outlining-your-notes-with-... (old, but you probably want the basics to get hooked first :-))
http://doc.norang.ca/org-mode.html (includes a good guide to the state of tasks, among lots of other things to orgify just about every aspect of your existence)
To install a GUI version it's "brew install emacs --cocoa".
Org-mode is perfect for taking notes in class, especially if it's a programming class. In that case, you could use Org-Babel[1].