Basically potted peonies have the advantage they can be sold while in bloom, and hence you can see exactly what you are buying. Out of my peonies all the Japanese tree ones and the Mackinac Grand were bought potted and the rest bare root. Zero problems.
Blooming is influenced by how old a division is: the larger and older (and more expensive) the sooner it will start blooming. Usually all nurseries with a decent peony lineup have a few older "ready to go" potted divisions that will start blooming right away. Again, it's all a matter of money and finding what you are looking for.
