Just the advice about Java hosting:
Many hosting providers who offer java hosting do not know what they are dealing with.
Often they can't help with configuration issues or having stability issues with java application server. I do not want to say anything bad about above replies. They may be very professional hosts, but I do not have experience with them.
So, the bottom line - try to find host that specializes on java hosting. There are actually many of them. They usually costs a little bit more then regular ones, but at least they know what they are doing. Also, you must ask how can you control your java environment. Is it private JVM or not? How many memory is allocated for you? Can you stop/start it yourselves? Can you at least restart your "context" if it's not a private JVM...
So, just make sure that host "understand" what are they doing.
You may not know, but last cPanel version includes Tomcat support and as result almost everybody started to offer java hosting these days...
P.S. Sorry if I sound very skeptical here, but I have several years experience with different java hosting companies