Most of the time is probably spent in the admin-ajax.php which loads all WP code. Basically, your suggestions will go as fast as a single page (with no cache).
I’ve seen 200ms as the fastest with keywords, and 600 ms with content.
There is no definitive guide book to speed up a WordPress site.
But, as it is a backend issue, you could try to identify the slowest parts of your site with a plugin like Query Monitor, or a server troubleshooting tool like New Relic. Personally, I’ve used New Relic on Cloudways, as it is installed and ready to use by default.