Can I transfer my marriage visa from my old passport to a new one, or should I wait for the new passport to apply?

You’ll need at least 6 months remaining on our passport expiration

I would say put OFF applying for the "marriage visa" until you get the new passport because it'd be better to have the VISA and the extension in the same passport once you start the process

Get the new passport, THEN apply for the 90 day Non-O visa and after that the year extension so that ALL those stamps are in the same passport (it will save time/effort down the road)

Plan your work, then work your plan.

Are you applying in your home country or in Thailand? Either way the initial non-o visa is only good for 90 days inside Thailand then in the last 30 days of the visa you need to apply for a 12 month extension of stay, that goes under consideration for a month then you get the extension stamped in your passport

Are you applying for an initial Non-O based on marriage, or a yearly extension?