Wow, congrats on your new job!! I wish you the best of luck! First off, lets deal with scheduling. There are always scheduling issues. Not enuf staff, staff wanting time off, etc. Where I work they have a system to fill in the kinks, they book extra staff in case of late sick calls, no shoes, etc. That way you are not left without staff at shift change.
As for moving from unit to unit, most Nurses will tell you if they don't mind floating. Personally I like having a home base, I feel I give better care with familiarity of surroundings and my patients. But again, this is a personal preference.
Introduce yourself to as many people as you'll be working with as possible. It's always nice to put a face to a name. You never mentioned if you were working in a big multi-disciplinary hospital, or a smaller nursing home kind of setting. Either way, best of luck!