Name the limit you need to remove
Do you need special services, custom configuration, guaranteed resources or unusual integrations? If the only reason is a slow site, first measure where the time goes (why your website is slow). Heavy code can stay slow after the move.
For a standard website, managed hosting can cover everything you need without separate administration. Compare specific features and limits, not just category names.

Plan for the work after launch
With your own server, someone has to own updates, backups, monitoring and recovery. A control panel doesn't make those duties go away. You can hand this work over to website maintenance.
Agree on access and the response process for outages. If the provider's support only covers the virtual machine, web server or application errors may still be your responsibility. That should be clear before you buy.

Test the setup under realistic load
Compare the key scenarios in the new environment: public pages, logins, search and integrations. Judge not just one fast request, but how it behaves at a normal peak and how it recovers after a problem.
A separate server makes sense when you have a specific requirement for the environment and someone who will look after it. That's when it's worth talking about server solutions. If there's no such requirement, start with regular hosting and compare plans using the tips in how to choose WordPress hosting.

