Hey Barb, is this stuff popcorn (accoustical texture) or what?
We know that whatever the stuff is, it is on drywall. So, that means it can all come off with not much adoo, but your looking at a messy job and alot of work and alot of money in labor.
I would like to convince you to leave it there, but its your home.
Are you removing all the texture on all ceilings? What are you going back with?
Lets say its popcorn. Then all you do is to get a garden sprayer and saturate the ceiling lightly with water mist, then with a scraper, start scraping off the stuff and it will come off easily. Then you, after the ceiling has dried out completely, re float the ceiling, then apply the new texture and then prime then repaint.
Now, this removal process is something that you could do, but the re floating and re texturing is something else. This could get into some big $$$$.
Come back with more info and we all will jump in more with details.