Hi,
Supposing that you've configured a filter for the search, and supposing that you've configured several columns for the search in that filter, there is no easy way to give priority to a column or another.
The order of the products on the search results depends on how you've configured the "ordering column" and "ordering direction" settings under the "products options" tab of the menu item used to display the search results and it's not linked to the search itself.
It would be diffcult to change that.