Starting task at an appointed time and date

[Copilotich]

Is there a way that a task can START on a specifit date and/or time?
Is the due date the only scheduling possible?
I have tasks that start on monday, (such as weekly revision, or monthly revision) that have a starting moment, (monday or 1st of the month ) and have a due date (sunday or last day of the month)
so far I have managed to set a recurring task that the due date is the actual due date (sunday or last day of the month) but the I would not see those tasks on today for example
There could be a special place on today list for started tasks with starting and due date.

If there is nothing like I explain I might open a new issue.
Otherwise, how you people manage to do this? I bet there are lots of you guys that use weekly reviews. How do you set that on SP?

:)