I use sheets of junk paper (e.g. stuff I got in the mail that is only printed on one side). I keep an "active" one that I cross stuff out from, etc. When I start a new one (about once a week) I go through the old one and port over any remaining items; most of the time I discard the whole thing since it's no longer relevant. If there are important items that are just too big to handle I'll transcribe it to my Calendar, Linear, Reminders app, etc.
To me this is a good balance of: - Writing things down is the major benefit for me, writing down on physical paper is even more helpful. - Forces me to garbage collect irrelevant stuff. - I don't need an app or even to buy paper really.