Search redirect to custom page

I am not sure how much you know so you can add to the following code, but I’ll give it anyway:

function allm_redirect_search() {

	if ( is_search() && isset($_GET['s']) ) { 

		// add some code to decide where you want to go, based on $_GET['s']

		// Go to other page:
		wp_redirect( LINK-TO-PAGE );
		exit();
	}
}
add_action( 'template_redirect', 'allm_redirect_search' );

Hope this gets you in the right direction.

The problem is if one of the suggestions is not picked, there would not be a page name matching the search term, so in that case you would want (I think) the user to go to the normal search results. It is only the auto-suggestions where you would want to go straight to the page, correct?

It makes more sense then to identify the auto-suggest function that inserts the selection in the search box and instead have it redirect to the associated page. JS/jQuery redirects are more flexible than PHP because you are not forced to only redirect before content is output.

JS/jQuery scripts can be overridden by ensuring your override is loaded after the script you are overriding. Using wp_enqueue_script() with a huge priority number will probably work, though identifying where and how the original script is loaded would be better.