Best way to install WordPress for Internet and Intranet sites?

I am planning to move a wordpress.com website for a pre-school onto a WordPress installation through our webhost.

At the same time, I am considering setting up an intranet site which would be accessed only by staff and committee members. This might include a document management system and would need to be accessed from within the pre-school setting and externally.

Should I have two separate WordPress installations – one for the internet site and one for the intranet – or would it be better to install WordPress once, and create the intranet part of the site by making the relevant pages private with some sort of log in requirement?

If the best way is to have multiple installations, should these be in sub-directories or sub-domains?

My website host allows me to install WordPress through a ‘one-click’ installation.