Rails 3.2.3 is compatible with Rails 3.1 and later versions. The main difference is a change in the default security settings (made in the wake of the recent GitHub mass assignment vulnerability—and, IMHO, long overdue).

If you want to get started with Rails, I suggest reading the Rails Tutorial, which I just updated to use 3.2.3:

http://railstutorial.org/book?version=3.2

If you're going to be working on a Rails 3.0 project, you can use the first edition of the book instead:

http://railstutorial.org/book?version=3.0

Screencasts for the 3.0 version are available at http://railstutorial.org/screencasts, and I'm planning to start on the 3.2 screencasts later today.