There is a tradeoff in choosing thickness in drywall. Thin drywall, (1/4") is very light and fairly inexpensive by comparison. However, it is not very durable during installation, and will transfer any bumps waves or abnormalities in the wall behind it right through to the new surface. Thicker boards like 3/8 or 1/2 are heavier and harder to work with, but are more resilient. Other items you will have to explore are the clearances for things like window frames, wall outlets,(depth requirements, adding a layer of drywall can make it really hard to reinstall a cover plate or an outlet in an existing box.) Door frames are also a consideration. Making a wall a full 1/2 to 1 inch thicker can make trimming out your doorframe a real nightmare.
You should remove all outlets and switches before you drywall, and be careful when you do this.
You might consider getting a bid from a plaster professional on just repairing your existing walls. I don't mean a hack repair, but hire a real craftsman to restore the walls if possible. Take advantage of the situation first, though and add any cabling or electrical you might wish you had done later. Consider TV, Phone, Home Theater, and a new one, CAT5 or computer cabling. Now is the time to do it!