Before answering your main question, I'd suggest one alternative: If the plaster is still firmly attached to the lathing but has a few cracks, I'd first try removing the texture paint. You might be able to saturate it with warm water and then scrape if off with a wide putty knife. Try a section. If this works but is too much work, try a wallpaper steamer. Then once you get all this goo off, sand the walls, patch the cracks and you're ready to go.
If the plaster is too far gone, you can remove it with a flat pry bar. I assume from your description the house has wood lathing. The plaster will come off fairly easily once you get going. (Be sure to wear a good mask or respirator, heavy clothes and leather gloves, though. And be ABSOLUTELY sure to seal off any ductwork -- and to seal off the room itself from the rest of the house. Plaster dust is nasty on the respiratory system -- and if you don't confine it to the room you're working in, it's a gift that keeps on giving. It'll get everywhere!)
The hardest part of this job, frankly, is doing a quality drywall job if you're a novice. You can read all you want about drywalling techniques, but the only way to learn to tape and mud walls decently is to do it. And frankly, your first room will, well, look as if it's your first room.
Some things that make the job a touch easier:
* Use water-resistant drywall.
* Buy the right tools, such as a full selection of drywall knifes, and one made for inside corners.
* Use self-adhering fiberglass tape instead of paper tape. It's easier.
* And use the super-whipped pre-mixed drywall mud. It doesn't shrink as much as traditional mixtures as it dries -- making it easier to apply.
As for re-grouting, it's a fairly easy job -- especially compared to those walls! You can use either a paint scraper with a triangular end, or get a tool specifically designed to loosen old grout. Someone at the hardware store or lumberyard can show you what to buy. Once you've removed the old stuff (a tedious but fairly easy job) then you mix up new grout, apply it with a nearly dry sponge and then clean up the mess afterward.
Good luck -- and again, unless the plaster is falling off those walls, try to work with it somehow rather than replacing it.