It sounds to me like your situation is perfectly suited for a server. A power user’s guide to OS X Server, Mavericks edition | Ars Technica provides an analysis for your consideration.
Another choice to consider is iCloud.
iCloud is the simpler solution. Everyone will need an iCloud account; then you can create a calendar and share it privately, giving subscribers the ability to edit it. Please see
and the subsequent pages.
Alterntively you could all use the same iCloud account, which would have the same effect. If anyone already has their own iCloud account they can sign into this one in System Preferences (or Settings)>Mail, Contacts and Calendars, so that the calendar will appear alongside their own ones, again with full access.