I recently moved my domain from a C-Panel hosted domain (and Email to Google G Suite to a self-managed Vultr domain and needed to transfer my WordPress site.
In these olden days of the Internet you just needed to submit your site to search engines and wait a few days and every thing was fine and dandy. Making your site appear high in search engines these days is next to impossible due to changing rules and formulas defined by search engines. There is no golden rule or trade secret to getting pages ranked high on search engines. You will need to do a number of things to get higher in search results or even appear on search results at all
I used to use WP Total Cache in the past but decided to check out what other recommended, I found this post 6 Best WordPress Caching Plugins Compared.