I do not know if I understood your question correctly, and I will try to give an objective answer, neutral and not based on opinions. But I confess that this is not one of the best answers that could be given.
What type of host I use to run JSP?
You can use Tomcat, Jboss, Glassfish, or any other container for Servlets and JSP.
Cpanel runs JSP automatically?
I think so. Maybe you can see more here: https://forums.cpanel.net/threads/cpanel-tomcat-jsp-and-servlets-guide.282922/ - I am not going to go into more detail about this, because I have no knowledge of it.
What I need to do to run JSP and PHP on the same server?
Just put the two to run on the same server. However, they should be on different TCP ports. A simple way to do this would be to run PHP on port 80 and your Servlets/JSP server on port 8080, for example.
In case you need everything at door 80, you can:
Utilise server side includes, which allows you to even mix the content generated by JSP and PHP on the same page, although this is not a simple task.
Place some proxy service (e.g., Apache) on your server at port 80 and use it to redirect requests to PHP or JSP at any criteria. JSP would be running on a port other than 80. PHP could be running inside Apache itself (or not).
Your question may be closed because you do not comply with the terms of the website (based on opinions). But I recommend Tegrator.
– Avelino