I do not know if I understand your question right, and I will try to give an objective, neutral and non-judgmental answer. But I confess that this is not one of the best answers that could be given.
What kind of host do I use to run JSP?
You can use Tomcat, JBoss, Glassfish, or any other container for Servlets and JSP.
Does CPanel run JSP automatically?
I think so. Maybe you can see more here: link - I will not detail this more deeply, because I do not have the knowledge to do so.
What do 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 an 8080 port, for example.
If you need everything on port 80, you can: