IMO, choosing pawpaws that are likely to have significantly compromised root systems and almost certainly inferior quality fruit, just to gain, at best, two years of production (and probably not even that), would not be a smart decision. If it were me, I wouldn't even consider the larger ones.

If you do decide to go mail-order, be sure to consider Nolin River.

Whatever you do, do not plant bare root. This is almost 100% fatal. The larger the pot the better since they do have a tap root. Also, shade is very important in the first few years of growth until its established. If you get two different varieites they should cross pollinate. To increase your chances place a roadkill animal around your pawpaws when they are flowering to attract flies; the main pollinator of pawpaws. Good Luck.

The Peterson varieties make much much better fruit than the huge majority of wild seedlings. Unless you know that their seed came from a great genetic background, the fruit will probably be mediocre.

I don't have any problem with Nolin River as a nursery, but their trees are bare root. I know Brandon, henceforth known as the pawpaw whisperer, has not had trouble with bare root pawpaws, many people have. I bought two from Nolin, planted one on the ground and planted one in a pot for a year. After three years, the one in the ground has grown less than 6 inches, and has never looked very good. I've done everything I can to baby it along. The one that spent a year in a pot is now in the ground, and has done great, producing 6 fruit last year while putting on over 2 feet of growth.

Anyhow, I would recommend getting the smaller plants, especially if they are potted. One Green World sells the Peterson varieties in small pots.

Alex

"Whatever you do, do not plant bare root. This is almost 100% fatal."

That is just simply incorrect!

As Alexander hinted at, I have never lost a single bare-root pawpaw from Nolin River. I have lost multiple potted pawpaws from other nurseries. If you do go with a potted pawpaw, try to find ones that have been air root pruned. Trying to chop out and correct pot-bound roots, in the case of pawpaws, is just an unnecessary mess, IMO.

Would putting the paw paw trees in pots under a oak tree that is 30 feet tall be enough shade till they get bigger?

That would be enough shade, but the trade-off of having potbound roots would be horrible. I usually encircle my new pawpaws with a wire cage (prevents predation/animal damage) and wrap that with a single layer of 50% shadecloth. I leave the shadecloth on for two years, removing the cloth from the top of the cage after year one.

I would strongly encourage you to plant your pawpaws out into their permanent location as soon as you get them!