Notes apps on Android seem good. I have experience of the Samsung Notes app and it's very good at keeping lists.
Personally, when I have done a particular task (or picked something up from the shopping list I compiled), I add a 'thumbs up' emoji next to it so I can see it's sorted.
If I want to be reminded of something, an appointment for example, I would set an alarm.
A quote for those blessed with a spouse:
I hope the new PM is kind to Larry the Cat
