I'm guessing you've found answers to your question already. But if you haven't, here are my two cents. Lol!!!
Pots, containers, and grow bags will work for what you want to do. But when it comes to access to plants and drainage, a fabric grow bag is your best bet. Considering that you intend to grow items like potatoes and carrots, which are both root plants, a grow bag with an access flap will work wonders for you compared to other bags that don't have access flaps other containers.
You can access the yield without having to remove the whole product in the bag, especially if you think they'll still do well. For instance, if you have two carrot plants growing in a large grow bag with an access flap and you check and find out one is ripe for harvest, but the other is not, will you take both?
A container doesn't offer this kind of benefit, although you might be able to deduce how well the yield will be by simply looking at the leaves. You can get a three-layer shelf with enough spacing to accommodate the bags, containers, and pots as you wish.
Looking at your options from a cost-effective perspective, I'll go with the grow bags, honestly. The cost of a pack of five 7-gal grow bags will be slightly on par with one container's price. Then you'll also need to deal with storing the pots for later use. Unlike bags, pots cannot be folded, although they may be stackable, but how much space do they take up, really?
It all boils down to preferences.