Actually another possibility is some sort of base that you plug your smart phone into so you can use it more like a land line - has a receiver, dialing, etc. like a real phone that you use instead of the cell phone. That would work too - anyone use one of those and which would you recommend?

I might suggest visiting your local AT&T store and seeing what's available. As you said, the choices will be very limited and the folks at the store will be much more knowledgeable about the latest, greatest offering from Apple, Samsung, etc than they will be about a "basic" phone. If you use a cell phone infrequently, one of "pay as you go" providers may be more economical.

I know of no device that functions as both a landline and mobile phone. Many cell phones will accept a corded headset, usually with a 3.5mm jack.

Consumer Cellular is a cell phone service for older folks like me who don't need or want lots of fancy stuff. They are cheap too. They run off of att but they are not part of att. I actually have a cheap smart phone that I got elsewhere, but they have plenty of basic phones for people that just need the basics.