I have inherited a 1950s house that has vinyl over original wood siding over old fiber board. Much of the house's siding is damaged and needs replacement. I'm thinking of replacing the full house's sheathing so I can re-insulate it and install new windows and Hardie siding or vinyl. The question is "is ripping off all the sheathing over doing it or the best option?" Also, what type of insulation and sheathing should I use? I'm located in Wichita, Kansas.
Fiberboard is flimsy and might be damaged in the process of removing the vinyl siding anyway. I'd replace it if the opportunity presented itself.
While you have the stud cavities open, replace whatever's in there with mineral wool. Then sheathe with plywood. Cover that with 2+ inches of rigid foam. Preferably polyiso (best R-value per inch) and preferably foil-faced (radiant barriers are nice, and you can use the foil surface as your water-resistive barrier if you tape the seams properly--no Tyvek!). Install your new windows on the foam, not the sheathing (outie windows). Install vertical furring strips over the foam, and nail your new siding into that. This creates drainage cavities that promote drying, and allow the foil surface of the foam to act as a radiant barrier.
Update: if after removing the sheathing and insulation, you discover that the wall was built with an interior-side vapor barrier (usually clear polyethylene sheeting right under the drywall), use a razor knife to cut it out. The wall assembly will be much more robust, especially in conjunction with the kind of exterior insulation I'm recommending.