You should put them in the biggest planter possible that you can still move.
I saw somebody who used 1/2 of a wooden barrel. Go to http://www.Freshops.com They have some photos. Read the info on the website it will answer a lot of your questions.
Most of the time the rhizomes are left in the ground. They develop an intricate network of roots that should stay undisturbed. Over the winter the hops in the ground should be covered with dirt & mulch. Year after year the get more vigorous growth due to the root networks ability to absorb moisture & nutrients quickly. Growth is a wopping 8-12" per day in June and July!!
If you have small containers you should try to bring them inside during the winter.
Hop rhizomes are cheap. $3.50 each. You could leave them there when you move out or take root cuttings. Or just dig them up and attempt to transplant. The time of your move would make a diiference in your decision. After April & May they will be growing like mad. You need to plant them in the ground around Easter.
Grow them one season and you'll know what you need to do.
I started with Cascade & Nugget. I harvested 2.5 oz of cascade and 1 oz the nugget. I have two plants each. These are the most vigorous growers and are Freshops starting recomendation. This is my first season. Two plants, one each grew like gangbusters and the others grew slow. All provided to the harvest. I will get another once or so before the first frost. Next year I should get tons 24-32oz. By the way the aroma is awesome when you harvest!!!
Photos of my hops: http://boozinsusansbrewery.spaces.live.com/
Drying is easy. I took an old dresser, pulled out the drawers, drilled large holes all over the drawers and then lined them with furnace filter cloth. I dumped the hops in the drawers closed them to just a crack and put a fan in the back to blow air through the drawers. They dried in less than two days, but I let them dry a week. The set-up was in the basement.
My wife thought I was obessed by how much care I gave them. Said somethin' like we wouldn't argue as much if I paid that much attention to her. I said if you start makin' beer I would!!!!