I think the only tricky situation is if there’s multiple people to coordinate, who want to add items while not at home, or go shopping on their way home. Other than that any simple (paper) note will do?!

I got an office whiteboard for the kitchen. I write down stuff that’s about to run out, or whatever I want to eat in the next days. And once I go shopping, I either memorize the items or snap a picture. No further software needed.