What's possible if I want to change my theme?

Good questions.

I do this fairly regularly.

Backup your current site, both the database and the files.
Create a new installation of WordPress and install it in a subdirectory of your choice or on a separate domain.
Then copy all of the files from your backup to your temporary subdirectory.
Restore your database to the new temporary database.
Update your wp-config.php file of your temporary site to point to the new database, which you just restored from backup.

Now you should be able to log onto the new test site and do all of the work you want to do. When you are ready to go live, you will simply need to backup your live site (files and database), just in case something goes wrong.
Move your new site to the folder structure of your original site. The database will not need to be moved. But you will need to update the location of the website in the database (or you can do it in the General Settings, just before you move the files). There are some additional database updates that need to be done as well.

Here is the official link to moving the blog.

[removed contact details – please do not solicit work on the forums]

You sound like the guy to know!

I’m completely out of my depth with all this so despite the awesome post (thanks!) I don’t think I’d dare try it. I’m sure to bungle something important.

Here’s my dilemma:
sandandseahomes.com

If you go to Properties for Sale and open ‘Lots El Sargento’ everything looks more or less ok – but I’ll soon have 2 or 300 under that category so the site will have a list of meaningless numbers on the left and nothing at all on the right (as you scroll down).

I’ve been thinking of buying this:
https://gorillathemes.com/demo/smooth/

But I’d want to get rid of the grinning realtor and get my current look and feel into that functionality.

Am I dreaming?

I haven’t worked with gorillathemes, so I don’t know how configurable they are. I have used genesis themes (a framework) with child themes. They are a little more expensive, but they have great flexibility, which may help you achieve what you desire.

The genesis theme and agent “child theme” may work well for you.
https://www.studiopress.com/demo/agentpress.html

No. you’re not dreaming. This is the great benefit of using WordPress. WordPress gives you the ability to customize extensively. But some of that customization depends on the templates or themes that you choose. Some are easier than others.

So, your steps are to pick your theme.
Create your backup (work-in-process) website based on your current website.
Add your new theme and your changes to your WIP website until you are satisfied.
Move your backup to your primary domain