You want a really big pot, otherwise they will become root bound after the first or second year.
Someone mentions 5-gallon above - will that do? Or should I go higher? Do I need to get any special plants to help with drainage?
Also, here's another question, somewhat related. I wanted to grow the vines up along the side of my deck, but after that I wanted to train them to go horizontally to form a sort of canopy over the deck. Is this possible?
I think that even a 5 gal is too small - You should think about a half barrel. This fall I transplanted 3 (Sterling, Willamette & Newport) 3 year old rhizomes. The main root masses were the size of softballs and there were roots running out 6-8 feet.