I don't even know if our agency have the right software to begin a
Sharepoint site.
We are running MS Small Business Server 2003 (I belive it comes with
Exchange), plus all the computers in the office have MS Office 2003
Pro.

I guess my first question is wether we can use our server with the
current software to setup a Sharepoint Site (intranet) or do we need
to pay for hosting outside the intranet because we don't have the
right software

I work for a non profit agency and as usual with this type of agency
we are way behind technology. All I know is that we are still using
pen and paper to do our team calendar and this has to stop, so the
idea is to create an "Team Calendar" online for everybody to share
their appointments.