Moving a site to an existing domain and new host

What seems to me like quite a complicated question – so I hope I manage to explain it clearly. Apologies if I don’t!

Our church has an existing non-WP website using a particular domain (e.g. churchsite.com).

I have developed a new WP site using a different domain (e.g. newWPchurchsite.co.uk) and now want to move it onto the existing domain to maintain continuity.

The new site will be hosted by a different company from the existing ones.

I would like to be able to transfer the new site to the current parish domain (churchsite.com) without making it live so that I can check everything is OK first.

As the 2 sites will be with different hosts, am I correct in thinking that I can set up the new one and, when I am happy it is OK, change over the DNS entries in the domain registration (churchsite.com) to put the new site live?

Also, while I have read the stuff about moving sites, I am probably going to take the cautious route of doing fresh installs of everything and setting it up page by page and post by post. Can I do this while leaving all the pages and posts as unpublished or, if I haven’t changed the DNS entry, can I just publish them anyway?

As I said, it seems complicated, so hoping you clever folk out there can help this, relative, newbie!

Thanks.

Steve