I want to get the most out of each chapter, so I don't want to inadvertently move on to Chapter 2 before finishing all the Chapter 1 side questions. Which quest should I do last (i.e. which quest moves the story forward)?
Chapter one of The Witcher 2 is a little funny in that it has several break points at which significant numbers of sidequests open up, or become unavailable, based on your progression the 'main' quest line. The quest order published at GameBanshee isn't the only sequence in which you can work, but it ensures you won't miss anything and provides a decent timeline.
To simplify it somewhat however:
You'll need to complete the first few steps of the Kayran quest before opening up a number of sidequests, so get started with that one quickly, but don't rush to finish it.
After that, delay the evening meeting with Laredo (for Indecent Proposal), and killing the Kayran for as long as possible. Completing those two quests triggers a chain of events that will reshape Flotsam, and allow you to finish a few outstanding sidequests, and close out access to several others. After that, things are pretty linear, if you've already done all the sidequests in your log, you should be good to go.