A wet or dry shop vac would be my choice. For $40-60 you can buy a high quality one, rather than paying half that to a tool rental place. I doubt that you need a vac with HEPA filters to accomplish this task, but I hope everyone is wearing adequate respirators during the demo and the cleanup. And by respirator, I don't mean a $2 dust mask that you get at Home Depot.

Shop Vac

Respirator

We got this one http://m.homedepot.com/p/3M-Mold-and-Lead-Particle-Respirator-in-Medium-1-Each-per-Pack-6297PA1-A/202078789

Taking precautions as much as we can. Wearing both breathing and eye protection. One thing the OH didn't do when he started was put up plastic sheets to limit where the dust spread. Now it's on both the first and second floor. :-( But, ceilings on the first floor will be coming down too so not too much of a biggie.

Now, can lime plaster go in the regular trash pickup? Don't think its go to recycling. Or should I contact the nearest dump/transfer station?

I have a follow-up question about building code requirements when you open up walls. Going to start a new thread on that.

The respirator in your link looks like a good choice. I can't answer your question about what your local landfill will accept, but the answer is probably "yes." If it were asbestos-containing, it would be a different story.