Should I record my helicopter and autogyro time in separate logbooks?
In the United States, except for that time which is used for certification or currency, the FAA permits you to log your time however you like, or even not log it at all.  That means that you can do pretty much whatever you feel like.

That said, here are my personal recommendations in order of how much I support them:


Get a digital pilot logbook. Log everything in it.
Get a professional pilot logbook with plenty of space for various categories and classes of aircraft. Copy all of your records from your old logbooks into it. Archive your old logbooks in a safe location. Use your new logbook for everything from here on.
Get a professional pilot logbook with plenty of space for various categories and classes of aircraft. Don't copy all the records from your old logbooks into it, just carry forward the totals. Archive your old logbooks in a safe location. Use your new logbook for everything from here on.
Get one logbook for each category/class of aircraft you intend to fly. Log your time in whichever logbook is appropriate. Remember which logbook is which. Keep them all easily accessible rather than storing them in a safe location. Worry about whether you lost one. Have a complicated system of adding up your totals from various logbooks. Make it difficult to look up flights chronologically. Feel sad.