I would like to be able to run a java program as Windows Service which uses a specific port number.  What is the minimal package and/or add-on option do I need?   Can I do it with basic plan + dedicated ip (9.95/month)?

You're asking for some very specific server capabilities there. I just want to make sure that you aren't passing on some marketing gobbledygook as firm requirements, and that you understand what you're asking for. The fact that you asked if the basic (Linux) plan would work leads me to wonder. If you're planning to actually use Windows Services, obviously you'd have to be on a Windows server. That might even require a dedicated Windows Server, especially if a specific port is required (I'm not familiar enough with the Windows side of things to say for certain). If you're in fact just using Java for your pages (rather than PHP or Perl), you might be able to use JSP (extra cost) on a shared basic (Linux) plan. If all you're doing is offering Java applets for download and running, any plan can do that. I say this not to insult you, but to make sure you're not loading on extra unnecessary requirements for your system -- some people buy far too much in a hosting plan, because they hear some buzz words and think they need those features when they don't (e.g., buy a Windows server because their PC runs Windows).