Thanks everyone for all the great advice.
I think I will postpone the liveaboard experience for a while and stick with shore based diving vacations until we are more competent. Will probably avoid Australia too, for COVID uncertainty.
Yes. Our Jamaica trip is a vacation first, with some diving. We're newly certified, so it will be our first diving in the Caribbean. I understand that Jamaica is generally considered a marginal diving destination. However, as new divers, I'm pretty sure we will find it fascinating. Cozumel will be our first actual "diving trip," where we're primarily diving. (I used your Cozumel trip reports and notes to plan our Cozumel trip.)
Jamaica then Coz is brilliant. You’ll be happy enough with what you see in Jamaica and then be comparatively wowed by Coz. My first trip was to the Great Barrier Reef way back when, and I swear nothing else can compare with that trip.