You almost certainly won't be able to run Java on your ISP's server - it usually costs quite a bit to host Java web apps.
You can, however, write desktop based applications in Java AND you can even write web applications and run them on your local machine if you download and install Tomcat
jakarta.apache.org/tomcat
I would STRONGLY reccomend, however, that you do not even think about writing internet applications until you have a good grasp of basic Java.
The thing is - Java isn't really much good on the desktop because it's quite simply too slow (unless you havea reasonably fast machine and plenty of memory). BUT web applications (where Java really comes into it's own) are slightly more complicated to write because they involve multithreading, networking code (in Servlets - kind of) and JSPs (different syntax - more like HTML if used properly, but they're ultimately Java classes)
Learn basic Java and practice on your local machine until you can write simple classes and maybe even the odd GUI or two (although that's not crucial) and then download tomcat and start having a crack at web applications. DO NOT even think about EJBs until you are strong with all of the above.
I write this as someone who teaches Java professionally so I should (hopefully! :wink: ) no a little bit about what I'm talking about!
Edit: OO in Java and C++ are exactly the same (conceptually - not the actual code) so their may be some value in learning basic C++
Java is much easier to write however and ,arguably, as powerful