Hi,
I would like to know if it’s possible to customize the search results page. And, if so, where should I begin? I’ll handle the coding. I just need a starting point.
The search results page is out of the scope of the plugin – it’s handled by your theme. Usually the best starting point is to make a child theme and modify the search.php file or the appropriate handler for the results page. Unfortunately it varies from theme to theme so there is no single good tutorial to go by.
Most themes do have options to change the results page archive, so for minor changes I suggest looking for that first.