Usually once your website starts getting 1,000 or more daily unique website visitors then it's time to start looking at a VPS hosting provider and move your website away from shared hosting.
You do need to know how to manage a VPS server though because running a VPS server is different than just hosting your website on a regular shared hosting account.
You should know how to secure the VPS server, install scripts and work the command line.
Learning a VPS server or dedicated server is very easy though once you start learning how one works.
I taught myself how to work servers and have a VPS server for my website.