Every group of page numbered in its own way (no number, Roman numbers, ordinary numbers, …) should be formatted by a separate page style.
You must first create the needed page styles.
According to your description, you can use built-in First Page for you cover (WARNING! First Page automatically switches to Default Style when end of page is reached) and Default Style for the bulk of the discourse.
Create a style for the unnumbered pages and one for the TOC. Give these styles the required properties (header, footer, margins, type of page number).
The key point is to cause a change in the page styles at precise locations in your document. This is done with “special” page breaks. You must use Insert>More Breaks>Manual Break. In the dialog, you can designate the page style to be made active after the break. You can also define the starting page number after the break.
A remark: things are intuitive when they fit in one’s habits, i.e. when they don’t hurt long-standing routines. Even when they are simple and “logical”, they will be qualified “counter-intuitive” because they shake non-debated “certainties”. When starting with a new tool, always learn the tool specifications. You don’t drive screws with a hammer, do you?
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