I agree with some of the other commentors - would probably rebuild entirely, maybe save the treads for reuse if they look decent. Cutting stringers and building stair railings aren't the easiest things for a beginning carpenter, you will want to read up on it and watch a few youtube videos at a minimum if you are doing it yourself. Use treated for any framing (the stringers etc), and then for any trim boards and the railings you will want to use something rot resistant that holds paint well such as cedar, or Accoya. If rebuilding the whole thing is a feels a bit out of your wheelhouse, you can certainly replace some of the fully rotted boards and then use a product such as Abatron Epoxy on smallish chunks of rot. Epoxy is fairly easy to use as long as you can follow directions, and it's a very high quality fix for minor rot. The bottom of the balusters and where the toprail is toenailed to the newel could good candidates for epoxy. Whatever you do, disregard any advice to use bondo, spray foam, caulk, etc to fill any large voids (haven't seen any yet...)