With Adobe Campaign Classic (ACC), reports often involve same skills as complex workflows or webApp.
Adobe Campaign Standard (ACS) reports are completely managed differently and have different capabilities (as they are based on Adobe Analytics reporting tools technologies). But I assume your question is about ACC.
If you need very powerful reporting tools, please also consider exporting ACC data and doing the dataviz presentation with Tableau Software, Qlik or Microsoft PowerBI.
That's being said, let me try to help you and point out to the key ideas below.
First of all, please have a look on factory ACC reports. Especially see the out-of-the-box deliveryStatistics report, it seems that it could be the closest of what you expect, apart the date range filter. This report is global AND mono-selection AND multi-selection (several deliveries selected through the user interface or other way). But perhaps you would prefer to start with the statisticsPerDelivery report if you find it more accurate.
So, for instance, see the behavior of this out-of-the box report deliveryStatistics when 2 deliveries are selected in the user interface and the report deliveryStatistics is displayed:
You can also do the same basic things at the operation level (all deliveries linked to an operation).
Please notice that it is easy to select all deliveries within a date period, through Adobe Campaign user interface, instead of doing it inside the AC report... I advise you to do it that way Because the selected deliveries will be automatically selected by AC context (UI manual selection, or by folder). The folder can be a deliveries folder "view" (Restrict tab).
Well, if you need for a specific reason to do the range date selection inside the report itself, please proceed as is:
First please duplicate the factory deliveryStatistics report, not modify it directly.
Then, add the Global checkbox:
Let's start by simpler use case, a date selection instead of a period of dates.
With the duplicated report, add 1 filter object for date range filtering (see screenshot highlighted).
For a date range, you must use Variables choice, so the query must be run again with the 2 date values saved as variables.
And the form must be displayed before the query. Or you can loop for displaying the results after selection change. Please have a look on factory reports, many examples are done like this.