I'd go with a popular framework at first. They all give you a built-in development server that will run your web app directly from a terminal.
Do you have any experience in anything other than C++? If so, try one of those languages first. In general, in my experience, familiarity is a great way to break the barrier into a new area.
If you don't have experience in the other languages (Ruby, Python, Go, etc) — pick a few common frameworks and built simple-stupid apps in them. Build a TODO app in Rails and Django. They are so quick to build you can follow tutorials and explore which one you seem to like most.
C++ is the language I usually use for day to day coding. I have experience in plenty of other languages but most of them aren't relevant for this task. No one is writing server code in Prolog. The only ones that would really apply would be Python or ML. I tend to use Python for small one off tasks that take advantage of its string manipulation abilities and hadn't really thought of it as being a contender in this space. I haven't used ML since I graduated so at this point I'd be starting from scratch with it and a different functional language might be a better choice.
Python is definitely a contender, don't discount it. It's not as dynamic as say, Ruby/Rails, but is certainly a good first web-type language. Flask is a good first step, since it's very simple. You can digest the Flask code as a rookie Python developer with relative ease.
If you wanted to veer off the beaten path of the big three (PHP, Ruby, Python), Go has some cool things going on, and you might find it interesting as a C++ dev.
I was going to suggest Django. I had been a back end developer for a while. I could put together a Perl CGI script to display a webpage, but not too much more.
One problem you first have with web development, is you see too many possible ways to implement something. Using a good framework makes a lot of these decisions for you (or at least encourages you to do things properly), and reduces the amount or boilerplate code you.
Plus the guys that write these frameworks have loads more experience than you and have added stuff you probably don't even know about. CSFR protection for example. Sure it was a pain getting the first errors resolved, but now I know that I ought to be including these things in my webpages now.
Do you have any experience in anything other than C++? If so, try one of those languages first. In general, in my experience, familiarity is a great way to break the barrier into a new area.
If you don't have experience in the other languages (Ruby, Python, Go, etc) — pick a few common frameworks and built simple-stupid apps in them. Build a TODO app in Rails and Django. They are so quick to build you can follow tutorials and explore which one you seem to like most.