Your official guide book is way out of date sky, so I guess its prudent to learn c-script first then lite-c as that is the only language we are going to have access to in the next 2 years or so.
So far it seems as though c-script and lite-c are pretty close prototyping wise but I dont know how pure mode would be to handle.
To start, find or ask for projects (test levels, scenarios etc)written in c-script, grab examples from the AUM series (later ones 36 onwards I think)and reproduce them untill you have the basics down pat then move over to lite-c at a later stage but keep in mind, c-script isnt going to be around for too much longer, its too limiting in a lot of ways.
Cheers...