It is best to remain active for as long as possible. Walking, balancing exercises and anything that works with core muscles are good. To help with swallowing, see a speech therapist early on, since speech and swallowing issues mean you want to keep your tongue and lips strong as long as possible.
A special note, because of the risks associated with blood pressure falling on rising and other cardio related issues, you should work with a physical therapist early on who is familiar with issues related to autonomic failure.