If you are looking to not have you Inbox bogged down with completed tasks, or tasks you have due in the future, the means to accomplish that is to run a filter, or a combination of filters, on your Inbox.
For example, if you run the filters for "Status" is 'Due' and "Timeline" is 'Current', then, simply hit the Save button, save it as a SmartList, and you'll be able to reference these filters and this specific list of tasks in the future and not have to re-run your filters every time you log in.
If you'd like that specific SmartList to load every time you open up the Inbox, simply load the SmartList and leave the Inbox page, and when you return, it will have that SmartList opened up for you!