I am trying to set up the first pages of chapters in a book.



On the first page I want the page number as a footer, and no header.

Thereafter, I want headers and footers.

How do I do this?

When I add the headers on the rest of the pages, it also appears on the first page.

I have ticked different first page, and am using section breaks to separate each chapter.

Assuming that you have your page numbers set up, insert a "Section Break" prior to proceeding to the 2nd page. Once in the heading section of the 2nd page, click on “Link to Previous” from the Navigation section of the Design toolbar and insert the Header for the Second page. Close the Header section the continue your text on the second page.

Here is a very useful link that will help: http://www.addbalance.com/usersguide/sections2007.htm. I know your profile indicates you are using 2016 but, this option in Word has been around for quite a while.

Note: I just noticed that you are on an MAC OS and I have no experience with them. Hopefully, this will not be an obstacle.

There is no need for a Section break, which will only complicate future edits. All you need do is specify a 'different first page' for the page layout (which it appears you've done) and not add the header to the first page of the Section.

Do note that, if the first-page header has the 'Link to Previous' or 'Same as Previous' property set, it will inherit whatever header the previous Section's first page header contains. Thus, if your document's first Section has an empty first-page header and subsequent sections have the 'Link to Previous' or 'Same as Previous' property set for the first-page header, their headers, too, will be empty.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]

I agree that no section break is needed for what you are doing. Sometimes section breaks are needed, but this is not one of the times. Each section has three different headers and footers available.
Header/Footer Settings Recap

If you are going to want to restart numbering or have Roman numerals on front matter and Arabic numerals on the body, you would want a section break.
Numbering Front Matter (Ribbon)