We remove all veg from plastic as soon as we get home. We buy paper sacks intended for the council issued waste food caddy. These are brilliant for storing any veg, especially outside in a shed or garage (no garage here, but plenty of shed space) Veg that is kept cool and dry seems to last well, as long as it's in tiptop condition to start with.
I sometimes buy sweet potatoes from M&S, the skins are always 'cleaner' for when I want a baked sweet potato in its skin. For ones that will be peeled any supermarket ones will do.
I think potatoes of any variety seem to be so varied. Some you buy last for ages, others are spoiling within days, and there's no rhyme nor reason for the difference!