Throwing away my To Do list- agenda items for people, and weekly To Dos

I’m in a job where I manage several people. Over the course of each day, there are agenda items for discussion with various people that come up. My To Do list includes a list of people I have standing meetings with where I capture these little items and use for reference at our next meeting (could be weeks away). I’m thinking I ought to keep this list to keep me organized… but wondering if there is a different way I should/could approach?

Also, so far as throwing away my To Do list, is it okay to keep a weekly To Do? I’m thinking I would then process that and a thought download weekly, then throw away the weekly To Do list. Or is the idea to not even have a To Do list? If so, how do I capture random things that come up daily that will require my attention?