"Baryta" is a technical name for barite, which is a mineralogical name for barium sulfate. It is white, heavy, completely insoluble, and fairly cheap. We use it by the ton as a weight addition to drilling mud in the oil industry.
All current fiber papers have a baryta layer, with one exception: Bergger makes an uncoated one - I can't remember the name of it right now.
This pre-emulsion coating has been used for a very long time, in fact I believe some of the earliest "gas light" papers were baryta coated!
As to toning: RC papers generally tone as well as fiber, but may be more reluctant to change of tone. Which might be a boon if you want archivally toned neutral black prints; try Ilford MG IV in selenium. Even Viradon gives only a very slight warming!