If you want to keep the integrity of the plaster, then hire a plaster repair person.
If you don't mind sheetrock, it is definitely cheaper and will solve a multitude of problems, unless they miss the joists or dont use long enough screws.
If I were doing the plaster, I would remove loose plaster (topcoat or basecoat), prime with kilz, use mesh tape or mesh screen as needed and patch smooth, sand, prime and paint.
It is skilled work. The problem is, a drywaller can do repairs to plaster, but may skip the priming with Kilz over water damage, because they don't know any better. This work will not last.
Don't use paper tape on plaster either, just the fiberglass mesh tape that comes in rolls.
Many plaster ceilngs have more than one issue going on at once. A knowledgable plaster repair person will address all issues, from water damage to poor bonding, latex over oil, loose or weak areas that need anchoring, etc....
Good luck,
Philip LaMachio
http://estateplaster.com