People who restore works of art are artists and generally have specialized art training and experience.

People who protect documents are called archivists. Very often they have their degree in library science with a specialization in archival studies. Many come from a background in literature.

There is also the field of historic preservation. Often concerned with the preservation of buildings and very often did their undergraduate study in history or architectural studies.

The degree you get could be a BA or a BS — there is no real difference here. From what you write, I suspect that a BA in either history or literature is what you’re looking for. Then some non-degree study in the trades of restoration or archiving.

Most often, the historians that study a particular area have a degree related to that area and some strong work in history. For example, a museum collection of musical instruments or printed music would be managed by someone (curator) who likely has a degree in music and has studied history as well.

Archeology also examines items of the past and works to protect and restore them. Many museum workers come from a background in archeology or anthropology.

Very many of the professional positions in the areas you’re considering will require a master’s degree and specialized additional training.

The American Association of Museums has some interesting reading about the profession. http://www.aam-us.org/

you need to know the reactions that will harm the work, and know what to use to stop or correct it.