Hosting is the computer the site runs on. For a WordPress site the real choice is shared hosting, a VPS you manage yourself, or a VPS someone else manages. A dedicated server is a different scale, and most small sites never need one.
Shared hosting
Your site shares a server with other customers. It is cheap, and someone else applies the server updates. It is a reasonable place for a small brochure site with little traffic.
The limit shows up as the site gets heavier. A shop, a pile of plugins, or a neighbour on the same server having a busy day, and the pages slow down. You also cannot change much about PHP, caching or the firewall.
A VPS you manage
A virtual private server gives the site its own resources. You can set the PHP version, the cache and the backups. You also become the person who patches the operating system, renews the certificate, and answers the server when it falls over.
A VPS someone looks after
This is the hosting I provide for WordPress. The site sits on a VPS. I set it up for WordPress, apply updates, keep backups, fit the SSL certificate, and deal with it when it is slow or down. You do not have to learn the server.
The details of that service are in maintenance and hosting.
Which one
Stay on shared hosting while the site is small and fast enough. Move when the slowness is the server, when you are taking payments, or when you want updates and backups done whether or not you remember.
Moving later is possible. It is fiddly, so if you already know the site will grow into a shop, start on a managed VPS.
If you want a view on the host you already have, send me the address.