You might keep a notepad handy and as you go through your day, jot down the things you notice that you would probably not be able to do without.
So far as the fabric diaper question...is the washer in your apartment? If not, how difficult will it be to access it as regularly as you need? Also, you say its furnished, will the cloth potentially cause more damage (from leaks) to those furnishings than disposable would? I have never used cloth diapers myself, so I don't know if that is a valid question or not!
Good luck with your move! Hope you find your new home quickly so you can settled.