I couldn't say about American varieties.
In the astringent the Hachyia is unanimously considered one of the best (we have one very similar in taste - the one in my photos, which sells by the name of "Coroa de Rei")
In the non-astringent, Gyant Fuyu, Jiro, O'Gosho and Hana Fuyu seem to have the preference of many but, in the end, it's a matter of personal taste.
Regarding shelf life - the Spanish tend to sell mainly one astringent variety in the supermarkets that keeps for several weeks (the cultivar is Rojo Brilhante and they sell it by the brand name of Persimon - not the best idea they had).
To be able to do that, they pick it hard (still quite unripe) and remove the astringency artificially (the process can take 2 days, and uses an atmosphere of ethanol in a temperature and humidity controlled room), so they stay firm for some weeks and can be eaten like the non-astringent (but in my opinion they do not develop their full flavor this way)