My biggest warning on mesh:
All mesh nodes will use the same channel as the gateway they're connected to. That means that worst-case your entire network will run on 2 channels... or you might get lucky and be able to mix some on 2.4 and some on 5Ghz... Neither is going to be a great experience unless you have very few devices and/or vary low bandwidth demands. This is going to create a massive "hidden transmitter" problem domain.
I second the push for as many cabled nodes as you can manage. 2 is better than 1, but 4 or so is probably a bare minimum for the 12 APs you want to deploy. You really want to make sure that each repeater can talk directly to a gateway.