They can sort messages directly with rules as they come in and then use a Search Folder to aggregate all the all the Unread Items into a single "virtual" folder. A similar method is described here:
Todays Unread Mail folder
Another way to sort afterwards would be to use Quick Steps. These can contain multiple actions as well (for instance; move to a folder, mark as read and mark as completed).
Yet another way to go would be to create rules which are disabled and run them manually at the end of the day or week. You can do this via the "Run Rules Now..." button in the "Manage Rules & Alerts" dialog.
Note that unless they are actually also deleting items, it won't do anything to the size of the pst-file. They can use multiple pst-files as well but that will only spread and delay the issue for a bit.
If you can't handle pst-files up to 50GB, you can decrease the maximum size and warning size via the Registry. See:
Increase maximum size pst-files