I don't put much stock in most of what I've read about native American or even colonial origin of particular cultivars of things. Most of it just seems overly romanticized and lacking in any real provable confirmation.
That said, here in Southern Indiana the only named potatoes I remember as a kid from 60 years ago are Kennebec and Pontiac. They were my mother's favorites and I know that my grandfather grew them, probably going back 100 years. That's a far cry from Indian and settler times.
As far as sweet potatoes, most any will grow here but I don't remember them at all as a kid. I think they are traditionally more a southern crop. I don't know if native Americans of this region grew them much at all, I would be interested in any documentation or stories that they did. They are such an easy and productive crop it seems to me that if they were grown much by the natives that they would be part of their generally accepted agricultural history along with beans, corn and squash. Sweet potatoes most often don't even make actual seeds, many don't even bloom. Propagation is done by saving
roots to make slips the next year but they are very intolerant to cold. Back then it would have been very difficult to keep roots alive over winter.
That's not a problem for us though cause we keep our houses above freezing all winter. Unless the historical aspect is of interest and importance, I would just get a few kinds and then keep propagating the ones I liked best. There is one called Georgia Jet and another called Nancy Hall and some from New Jersey whose names I've forgotten. They have been around a long time but no where near back to settler or native times, I don't think. I suspect that back then they were only grown in areas that didn't freeze in the winter, they are
perennial in those places.
Actually I breed sweet potatoes and have done a LOT of research on them but it was mostly focused on how to get them to make seeds, I just glossed over anything else. I'm making a mental note to dig all that out this winter and go through it to see if there are hints of when they came to be cultivated and if there are any named varieties still around that date back that far.