Ahh, don't we just love group projects!
To add to what Visvanath has already said, if you install a Moodle server to your laptop, then you will need to set it up so that it can act as a server on a network. We didn't do that, so never got it working like I wanted it to because the laptop never had a static IP address, which I did not know was important, at that time. This can be a difficult process but can work none-the-less. You would be better off if your tech guys can set up a separate PC as a server, then using that as your test Moodle. This does not interfere with your main server, and if your security is set correctly, unless someone knows about it, they can't access the server, let alone the Moodle. Talk with your tech guys as to the best way of doing this. You don't need a new superdooper PC just anything capable of running Windows XP or Linux, or an older Mac, I think should be sufficient.
For everyone to have access to the Moodle server, and the codebase, all they need be is Administrators for that server. To access all areas of the Moodle, make them all Administrators, and that should allow you to do what you need to do.
There is just one difficulty with this model. Documentation. People do not always provide sufficient documentation about what they are doing, so they change something and the site stops working. Always happens. Inevitably, someone gets upset and problems arise, so you must absolutely insist that anyone who has access to the codebase and the site as an administrator documents everything they do while they are doing it, NOT afterward, its too late then. Good luck...