Hi, Jared:
I garden in a relatively small suburban yard (with a very picky homeowners association). However, I've been growing potatoes for several years in 15 gallon smart pots. Potatoes can do well in large containers with a loose potting mix. I don't even have enough real-estate to let my vines sprawl, so I use double-ringed plant supports on the outside of my smart pots, and run a length of cheap plastic net-type fencing around the supports. My vines all grow up and stay contained, and I plant flowers outside so no one can complain. I use straw or mulched leaves to keep mulching up as the vines grow--you don't want your potatoes exposed to the light.
Potatoes are fairly heavy feeders, so keep that in mind, and need a consistant water source. There is a good guide to see how big of a seed potato to plant at
http://www.potatogarden.com/
When the vines start to flower, you are starting to get baby potatoes, and can dig down to harvest some if you wish. Otherwise, wait until the vines start to dry back to harvest. Dig carefully so you don't damage the potatoes and they will store well. I keep mine in our basement, which is not terribly cool.
Do a little research to see which varieties are known to keep longer. Give it a try--you'll be hooked!
