[pushkins]

Okay i see where you found the correct name for the ceiling that you are trying top create. "Tray Ceiling"

Yes you are absolutley right , removing the plaster and lathe is and will be a very messy job, it can be made a little easier by having a plan of attack and the right tools.
1.Put up plastic across any doorway or opening to other rooms.
2.Put down cardboard or thick canvas drop cloths on the floor.
3.Wear a FACE MASK at all times.
4. I find a spade is great to help peel off the old plaster, run it underneath the layer of plaster.
5.Use a flate crow bar/jimmy bar/pinch bar to remove the lath and either remove or hammer home the remaining exposed nails.

The main problem around studs is that when they were building many of these old homes with plaster as a finish they didn't need worry too much about straight walls as the plaster would come along and for the most make all the walls flat, as your removing the existing plaster take notice that sometimes you will find it thicker in places and thinner in others, good plasters had a great eye, it is an art.
The problem nowadays is that when you renovate an older home with drywall and you come across not so desirable studs, you are fairly limited in what you can do.
1. Run a string from one end to the other and first determine if and where your highs and lows exist, you might be able to shave a little off with a planner if it is only a couple of low or pushed out ceiling joists or wall studs.
2. If there is room between the string and the joists/stud you can always pack that out with shims or old lath strips, it all depends on just how much you need to go.
3. Ceiling joists and wall studs can be sistered onto with straight wood as you mentioned you could nail them for the ceiling though I personally screw as well as nail. 2x4's are fine for the ceiling just make sure you attach them firmly to the existing joists. Same goes for the walls, but here you need to take into consideration electrical circuits passing through the existing 2x4 wall, if needed notch out the new stud to safely clear any electrical cables.
Just remember though when you add sister studs/joists you are changing the 16" centers for screwing on the drywall, depending on what side of the stud/joist you attach to you may have to cut your drywall a little more narrow . For example if your 1st joist is 16" from the wall and you sister on a new joist it will now be 17.5" or 14.5" away now depending on what side you sistered it.
As for your insulation, here it is your pick, code says it needs to be R13 for the walls, so you could use the spray on foam (it's not cheap) If you want to keep the cost down use R13 roll or piece insulation and yes you do need a vapor barrier for the walls the paper must face to the heated area ie: face the the room.
Basically a vapor barrier helps prevent condensation forming in the walls, which is one place you really don't want moisture building up.
If your exterior walls are brick then you will need to make sure the insulation doesn't touch the brick wall.

Hope this helps you.

Good luck !