A student recently asked me for advice on getting up to speed quickly reading Chinese. I figured I’d share the comments here because it might be useful to those students for whom the material on WordSwing feels a bit out of reach. This advice relates primarily to reading, as that was this student’s interest, and it’s biased by my own preferences and experiences.
I’m a fan of graded readers. The first good (and perhaps still the best) graded reader was by DeFrancis, Beginning Chinese Reader. These are two volumes (Part I and Part II) and they introduce about 400 (traditional) characters. There is a revised edition that has been updated to be more modern and less literary. These books are just for learning characters and practicing reading. They are very well designed.
He also wrote books that go along with them (i.e., use the same characters) but which introduce basic grammar, and the readers are careful to keep pace grammar-wise with the text book. I’ve never read the grammar books though because by the time I discovered the readers I was familiar with Chinese grammar, which is actually rather simple. A good grammar book is Modern Mandarin Chinese Grammar.
You might also be interested in Heisig's books on learning characters. He has a very particular method for relating the constituent parts of Chinese characters to stories as a way to memorize the large number of characters. I don’t particularly recommend following his method exactly, but some vague familiarity with his ideas is very useful.
John Pasden’s Mandarin Companion graded readers are also very good. If you were to work your way through the two DeFrancis readers, a grammar book, and some of the Mandarin Companion books, then all of what WordSwing offers would be well within reach.
PS: Look for used copies of these books if you’d like to save money.