I mentioned your rifle to a friend of mine who is into model 99s, and he felt it would be important to identify the model and age if possible. It seems some specific models of 99 are rather rare, and of considerable interest to collectors, in any condition.
pics are always nice, but I know, not always possible. Shape of forend, barrel band, or not, factory drilled and tapped or not, ser# (xx for the last digits), other marking and locations and any other information would be a big help.
Certainly find out before going to a major step like rebarreling. Let us know how it does in its present condition. Worn looking bores sometimes shoot accepably well.
Good luck with your project.
All else being equal (and it almost never is) bigger bullets tend to work better.