Of course you can use any size containers that are managable for your situation. Be sure to use a good rich potting soil.
And as for cutting the vines back, I wouldn't cut them any shorter than six feet, but eight feet might give you a better crop.
The stem will continue to grow and you will need to cut it back about every 10 days, and this will keep the vine growing strong in the laterals and in gourd growth.

Jan

Could you possibly give me a recommendation on approximate size containers? In terms of gallons or pot diameter. You say "any size containers that are managable" however, without me being a smart a$$ I'm certain there is a minimum size. I'd just like some idea as to what I should shop for.

Having tried containers a few years ago, with poor results, I wouldn't recommend any thing that holds less than 2 gallons of soil.
3 - 4 gallons might be best.
Be sure you have good drainage, and a good blend of soil.

I like to mix potting soil,(4 parts) (any brand) with peat moss,(2 parts) vermiculite,(1 part) and top soil, (1 part).
I use this when potting most plants, whether transplanting from my starts or what I bring home from the garden center.