The easiest thing to do here is what Laura suggested. Having sub templates that have the different zones is going to be much easier, plus that is really what the templates are supposed to be for. A master page is mainly for the header and footer of a site, so if that look and feel is the same, then no reason to create another master page. Create one page template with a zone for the menu, and another without it. Then assign either one of those templates to your pages and you are done.
If you need another variation, then you just clone the template, and add to it or remove items, then you assign it to the corresponding pages. Just make sure that when you make a change to a template, you are aware of the pages that it will affect.