Yes, the locally installed MAMP package from Moodle.org would allow you to develop courses. Then, when you do have a server setup, backups from the local MAMP server could be restored to the server. That isn't that techie. ;)
As far as a hosting solution for Moodle, one could Google for that, but maybe the one that is 'right' for your needs is SiteGround. Affordable packages and they have a form to use in installing Moodle. Just make sure the local version is either a lower version or same as what runs on the server. (locally developed courses in version 2.4.1 may not be restorable to a server running 2.3.x)
https://www.siteground.com/tutorials/moodle/
You should know I don't host Moodles with SiteGround but there have been some folks in these forums who have/are.
In looking at their offerings, my only concern is having enough 'umph' to run a site for 5 teachers and their students ... depends upon number of students, etc..
Cheap is good for pocketbook, but sometimes one gets what one pays for! Every journey begins with one step ... so start walking! ;)
'spirit of sharing', Ken