What is the best way of breaking a mathematical development into a sequence of articles?
Each journal article should "tell a story". Break the thesis up into coherent stories. 

It looks like you're already doing that. The first article concentrates on generalizing the classical theorem, and the second gives the results that are relevant to current research.

I would suggest just putting the groundwork you need for the generalization of the classical theorem into the first article (unless you can save a lot of space by developing some of the groundwork for the second article at the same time as the groundwork for the first). And you should definitely mention the second article to provide more motivation for the groundwork. But putting groundwork that's not needed in this first article will detract from the "story". 

In the second article, you should include a quick review of the groundwork developed in the first article, and refer the reader to the first article if they want more details. Then add the extra groundwork needed for the second article, and  proceed to the results of the second article. 

One comment from experience: if you put a result that does not fit the "story" into a paper, when people read your paper, they are very likely not to even notice this result. So it's much better to put it in a separate paper. 

On the other hand, as you can tell from the comments here, many people consider it bad form to spread one story over two papers. So you should split a long result into several papers only if you can formulate it as several related "stories".