You can do cgi programming (a cgi is a plugin that handles http requests and returns the HTML for a web page) in C++, but it’s not a popular language for web programming, nor a particularly good way to learn C++ (C++ shines on larger programs, generally).
You can write Java Server Pages (JSP) in Java if you like. I’m not sure how popular that is these days.
Microsoft’s ASP.NET allows you to write server-side applications in any .NET language (C#, Visual Basic, C++.NET, probably a few others).
Perl, PHP, and Ruby are common for these things, too. Ruby supports a framework called “Rails” that basically does the basics for you, and you just “customize” to your liking. Rails is trendy today, but I suspect that PHP is far more common, so if you’re looking for something specifically as a learning experience, PHP/Perl is probably a better choice. Python is also fairly common. All the “P” languages are both relatively simple and somewhat similar – you may want to just take a couple weeks and learn them all.
All that having been said, the place to start is your ISP. They’ll determine what you can host and what you can’t, so not all the above options will likely apply to you.
If you’re doing this primarily for efficiency of having the final app, I’m guesing that AJAX or PHP + MySQL (there are books specifically on these combinations) will be your best bet.
If you’re doing it primarily to learn skills that are commercially valuable, I’d start with ASP.NET, AJAX, and Perl, then add Rails and PHP. Databases (if you need one) are simpler: MySQL, Microsoft SQL Server, Oracle (not in the price range of a small developer, although I think they have a free one), and PostgresSQL are some of the options, and they’re all very, very similar (SQL is not as standardized a language as most others, so solutions are often not portable, but they will be very similar from one system to the next).