Talk to your SM about what they expect of you- that will help you figure out what paperwork you need to generate. (Prop preset list, quick change plot, etc). Your book is a way to organize that information- set it up in whatever way is most useful for you to keep track of everything. For me, this means my book as an ASM is pretty much exactly the same as when I SM.
I think it's generally helpful for ASMs to have a thorough understanding of props, costumes, anything to do with running rehearsal, and anything to do with running backstage. But on some shows, I might want an ASM to track script changes, projections, run rehearsal sound cues, or any number of other things- it really depends on the show (and how many ASMs there are). I also like to have my ASMs to have some idea of the blocking- even if they are not primarily responsible for it, it can be helpful for any number of other reasons.
I keep frequently used documents in clear plastic sheet protectors- like the daily schedule, contact lists, etc- easy to grab. Anything that I need to carry around during rehearsal (like a prop preset or running list) I stick onto a clipboard. I've spiral-bound an opera score before but never a script- it did help a lot in rehearsals where I was literally running back and forth cueing entrances.