Changing the ORDER BY in WordPress default search function

My client’s website has a blog category and many product categories. She would like the search results to include the blog posts, but have the product posts first.

I can see two major implementation options

  1. Change the search query in functions.php
  2. Resort the search query results in the search.php template file

My question is: has anyone implemented this task, what implementation method did you use, and what issues did you have in the process?

I have searched for an answer to this specific situation and come up empty.