Yup, start simple.
Animation is the obvious place to start. Then look at simple actions with buttons. Then after a few weeks/months you could dive in to some deeper action script. There are a lot of cool books out there that can help you on your way.
Thomsons small project is a really good idea though. Why not make a really simple portfolio site, with a simple button menu system for starters, then as your knowledge increases you can add new features, fades on the images, funky rollovers etc. etc.
The other thing I would say is to remember to keep everything organised. Be meticulous, folders in the library, well named layers and relevant naming for symbols and instances (adding extensions like _mov _gr _txt can be a big help when you have lots of them) it gets more and more important the larger your projects get. Dull and time consuming it may be but it does pay off in the end.
Good, luck and if you need any help you know where to come
