Most task management apps with any meat on them will let you have both dated and undated tasks. In those cases, it can be a temptation to start adding deadlines to every task - even those that don't really have deadlines. I suggest that this is a temptation you ought to resist.
Pocket Informant, Todo, Toodledo, Google Tasks,.... These are just some of the major task management apps that let you have both dated and undated tasks. This makes a lot of sense, because knowing due dates are an important part of deciding what to do next. People will often start with whatever needs to be done that day, and then, time permitting, worry about other tasks.
But there is a temptation - I feel it myself - to assign due dates to tasks that don't really have them. That is, one may decide to assign a due date to a task not because it's actually due on some date, but because one merely wishes to be able to do it by then. In combination with start dates or horizons, the temptation becomes even greater.
For instance, I need to call my aunt in Italy. There's really no hard deadline for that, but I would like to get it done "sometime this week." So I set it as a task with a start date of Monday and a due date of the following Sunday.
While that may seem perfectly reasonable, it can create a trap (which even I have fallen into - more than once). The trap is this: as you assign due dates to more and more tasks that don't really have them, it becomes less and less likely that you will ever get to your undated tasks; and that can easily lead you to adding due dates to more and more of your otherwise undated tasks, just to increase the odds that you'll actually do them. You end up, in the logical extreme, having due dates on all your tasks, and not knowing which due dates are real and which are only your preferences. And that rather defeats the purpose of having due dates at all, doesn't it?
This also highlights the difference between a task's due date and its significance. Some tasks just have to get done, even though they don't have a proper due date - getting one's annual physical examination, for instance. Other tasks may have a hard due date, but the task itself isn't so significant - for instance, buying a new suit while a sale is on at your favorite clothing store.
This leads me to my preferred solution: I use due dates only for things that actually have due dates, and I use priorities - or whatever other mechanism afforded by the tool I'm using - to rank significance. It would be nice if I could separately rate the amount of work required to complete a task (something I've written about before), but it seems that that's just not in the cards for now.