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I use Apple Notes and Reminders. The Reminders app is actually pretty robust and is also good for your grocery list etc. (you can add items via Siri). The main reason I use it is because reminders stay front-and-center on my Lock Screen even after I unlock and re-lock my phone. I have yet to find another app whose notifications don’t get buried in the Notification Center.
How do you add stuff to a reminder, especially using Siri?
Right now we're using a shared Apple Notes so anyone in the home can add items for me to buy. (Yes, I hate that feature but here we are… ; )
I do the same as @veedems already posted; name the list whatever you want and tell Siri to "add X to my Y list". Also works for a to-do list etc. One benefit of using Reminders over Notes is that you can pull a Reminders list up on your Apple Watch, if you have one. That way you can have your shopping list on your wrist in the store instead of pulling out your phone.
Great tip about the watch option. Thank you!