There is no order of precedence. A motion can be adopted by a committee to undertake a study and the study might never be done, because of a lack of time or because there are other emergencies. As for the private member's bill, if it's referred to the committee, the committee will have 60 sitting days to report it back to the House.
The committee can decide to do the private member's bill first and the self-initiated studies afterwards, or otherwise. The calendar is up to the committee. As I said, by standing order, the committee has 60 sitting days to report a private member's bill back to the House.