Ok that is a bit different.
One thing to take into consideration with a non-tech environment like a hospital is Support. You are going to need to have some form of Support SLA. Depending on the level of "patient critical" information - this may need to be 24x7. but whatever it is, there will be costs associated with this.
That is a variable cost that I would ask to have covered.
I'm not sure what you mean by "outside software". If you mean the cost of software that tracks Support Incidents and similar tactical OpEx costs, you probably can get them to pay for the Per Support Rep costshttp://www.phaseware.com/pricing
which will start at around $50/seat/mo up to $200/seat/mo - and you probably can get them to pay for the Client Side website.
You could of course Roll Your Own using OpenSource http://sitracker.org/
but the old adage of "outsource everything that is not your core business" is probably applicable.
You should give then a set of initial training for free, but you should have an agreement that they pay for additional training if they bring on staff or expand the program.
I would also offer them a discount for the first year if after the Betta they opt in - IF they give you a publishable case study
I would also give them a certain number of free feature requests, but then have a chargeback for certain types of customization