I live in a 1950’s home with old double hung windows. The windows are painted shut and a few are broken. We have saved and are ready to upgrade the windows but are not sure of the best approach. We have lathe and plaster inside and stucco on the outside.

I have replaced windows like the ones you have described. I wish I had understood the difficulty of the job before I started. Here is my advice to save you time and money. As you describe the wall components I know how fragile they are and how difficult it is to change. The best approach is to stay away from the stucco and lathe and plaster all together. I recommend installing inserts into the existing frames. An insert is a sealed unit with a vinyl frame but no exterior brick mold or nailing flange. You simply remove the existing window and tracks that the old windows slid in. Next install the insert into this opening and seal it in place with caulking and quarter round or similar trims as directed by the window manufacturer. The new windows will be a little smaller but they will appear larger as they will be new and shiny.