Like rememberthemilk.com ? You can make different tabs for things, and name those tabs / lists, and check them off, make notes, assign them to people, etc. It's a freemium model, and I've only ever used the free version. If you want an app you can pay to allow it to update more frequently. Since you want to keep phone use down, that shouldn't be a problem.
I've used RTM for tasks lists for various jobs as well as "to do soon" and "to do eventually" lists.