A five gallon bucket wouldn't allow much space for the tubers to develop. I'd go with a rectangular tote that gives bigger surface area and more soil.

The vines don't need to make contact with the ground. But they often re-root and you get some extra potatoes that way. Not sure how that would work with containers, but it happens when they're grown in-ground.

I've read that containers work fine. You'll want deep ones. Think about the size of an average sweet potato, and then imagine you'll get about 6 of those from each plant. I guess that will tell you how much space you need.

Since you've never grown them before, be sure to read up on curing and storing them. You need to cure them in a warm place after you dig them, then store them in a cool location for 6-8 weeks so the sugars develop.