Personally, my mental to-do model consists to a pretty large part of recurring tasks with more or less vague "deadlines."

For example, at home, taking out trash, watering plants, stocking up on groceries, paying the rent, etc.

However, almost all to-do systems seem to be aimed at scheduling one-off tasks.

So I would like the to-do system to more accurately model my real to-do model, which would probably mean having a special item type for these circular, Sisyphean tasks.

I use Toodledo [1] for this, especially for the recurring tasks. There are even different ways to define how it recurs, eg taking out the trash might be every Wednesday, but watering plants might be "2 days after I last completed it". When you complete the task, it automatically enters the next recurring task for you (and hides it from you until the appropriate day).

[1] http://www.toodledo.com

Potentially, at some point (i.e. not the MVP) as a "power user" option.

For the MVP, I would simply order by the Due Date, with "Important" (starred) items jumping to the top of the list (and if there are multiple "Important" items, they get ranked by Due Date. "Overdue" items (i.e. where the Due Date is in the past) would get jump over the "Important" items.

So, in this mock-up - https://disruptdecentralisedisintermediate.files.wordpress.c... - you see a bunch of items ranked by Due Date (i.e. the ones towards the bottom of the list have a Due Date further in the future), with an "Important" item ("Draft product roadmap presentation") above the others (even though it is Due _after_ the "Get milk" and "Call Cynthia.." items) and the "Call Joe Bloggs" item appears right at the top (and is highlighted) because it is Overdue.