If you're setting up an all new system you need to find out how the users are currently communicating in house. Besides the intercom and phone system. Then since it's a hospital pay attention to what they're going to use the email for - whether it's strictly in house or to communicate with the public - but security needs to be in mind every step of the way. IMO.
I don't know what the foundation of the system is - hardware (is it old new blah blah) - but first pay attention to the network hardware. Those routers and hubs may not be able to do the job - 512k just won't cut it anymore in most cases. You may need to add more or replace what exists. Those will also give you a good idea of the shape of the existing systems - if what you're working with is fairly up to date then most likely you won't have to deal with too many legacy issues with the hardware.
The operating systems on the workstations and what they're using for network security already would be next. Look into and be ready to deal with known issues between the operating systems and the email server software. Then the email service and network security - be prepared to reconfigure or even reinstall or replace that en masse.
And the users. People love new toys but there's always someone who'll try to break yours. The odds are there so I figured I'd bring it up. Make sure to take the time to set up procedures that are simple and effective. Keep a solid list of names and passwords - they are most likely to be lost or confused or forgotten the first two weeks of deployment.
Custom software. Keep that in mind too as you make decisions. Even if it's not your stuff to oversee - make sure to know that stuff in and out. Odds are it's mission critical and they must have it - so be very certain that your new service doesn't hinder it's use, effectiveness, or create issues.