We are paper people, also. It’s the simplest for us even though both of us have spent our entire working lives in technology.
For me, the act of writing something down helps me remember better than when I type. Once written, I actually don’t need the list any more unless we’re buying non-usual items.
Paper for normal groeries, Notes on iphone for Walmart and friends. I keep the lists adding items brought to my attention.
Big bugbear in my house: You are welcome to consume and enjoy anything you find in cupboard and fridge. BUT if you finish something or notice that the end is near, REPORT IT!
We use a shared family calendar app called Cozi. It comes with a list feature too so you can create different lists and all the family members can edit it. We have multiple lists, one for each store we usually shop at, like Sprouts, Whole Foods, Costco, etc. We just add things as we need them, then whoever goes to the store can use the list. It also has a shopping mode on the list so you can check off the items as you buy them.