The intent is to use them as a wall cover to cool off the yard and also hopefully provide food for us at the same time. (Although I'm pretty sure it's too late for a harvest this year.)

Should I keep them inside as houseplants til next spring? Put them out in a big pot now? Just plant them in the ground so they'll climb up the walls as planned? If I do that, will they produce sweet potatoes next year? (Are they perennials, or do I need to start them over next spring? And if I need to start them over, can I start with cuttings from the current non-producing vines?)

Obviously, I'm a total newbie at this. Any help/advice is appreciated!

Sweet potatoes (ornamental and culinary) are generally perennials here. Mine survive the winters just fine (though in "cold" (for here!) winters the foliage gets damaged or cut back). If your plants are indoors now, I'd wait until autumn before getting them outside. It would be such a huge change for indoor-grown plants to suddenly go outside at this time of year. In autumn you can ease them to life outside in their final location. They'll go dormant in winter but should survive just fine. If you're nervous, or in a colder part of AZ than Phoenix/Yuma, you can definitely use stem cuttings rooted in water to start new plants.

Let us know what you do and how it works out. Happy gardening!

Another question I didn't realize I had: How do I know if they're ornamental??? I sprouted a yam/sweet potato (who knows what it really was, as they're always mislabeled at the store, and I have no idea what the difference is anyway...) from the grocery store. So I assumed it would produce more sweet potatoes (or yams). BUT.... The leaves don't look like the leaves on all the other sweet potato plants I've seen pics of here, so does that mean it's an ornamental variety that won't produce edible potatoes?

The leaves are dark green with a little purple in them and more heart-shaped whereas the other plants I've seen are lighter green and have pointy leaves.