Doing it all at once would be cheaper.

But what exactly do you mean by "full home remodel"? Is it tearing everything down to the studs? Is it moving any walls?

Or is it just redoing the bathrooms and kitchen? And maybe replacing the flooring and painting throughout the rest of the house?

I'd suggest changing your post title (if Houzz allows you to).

The services that contractors would prefer to do would be the one that makes them the most money for the least amount of work. I was wondering why you'd care about that, so I clicked the link and found out that your actual question was totally different.

Your question in your post is what order should you do things.

The two are totally unrelated. :)

You can't do a full home remodel - because you don't have enough money - otherwise buy a new home.

Just for the heck of it - how much do you have to spend? Don't say "I'm not sure".