You can very well learn C++ without learning C, but be aware of the difference both in the way of syntax/available functions and the paradigm of thinking (structured vs. object-oriented). IMHO it would however benefit to learn the structured non-oo parts (of C++) first, and it's actually easier to learn them using C. Besides, if you're going to program for Unix/Linux, most of programs - and the OS itself - are actually written in C. If you decide to go with C++, I would also take a look at the Qt library/framework and it's companion RAD, an great way for making cross-platform GUI-applications with C++.
Not sure I'll include HTML as a *programming* language...
Personally I prefer C++, but as much as it pains me, I would have to say that learning Java (which is *different* from JavaScript, much used together with HTML and CSS to create dynamic web-pages) would be your best bet. It's much used and much sought-after among employers. It's also not that different from C++, so it will give you a leg-up if you decide to later learn C++ (or C) - and vice versa.
C# is another much used language. It's similar to C++ (and thus also C and Java), and much used for making Windows-programs. So if you plan to mostly make Windows-programs, C# is your best bet.
If you're more thinking about web-design and web-programming; learning HTML (especailly HTML5) and CSS (CSS3) would be necessery. In addition you should learn the server-side scripting languages (programming-languages) PHP (used on Unix/Linux-based web-servers) and/or ASP (used on Windows-based web-servers, and pretty much VisualBasic). In additon you should learn JavaScript for client-side interaction, and perhaps Java for making applets (programs downloaded from the net to be run "inside" the web-browser - like chat-application and secure log-in for banking services).
Python is a good language for just "throwing something together" - you can even make nice GUI-programs with it - and it's easy to learn. Very good for quick fixes for smaller tasks. Ruby is another language that fills a similar niche, but also is used quite a lot on the server-side of the web. Perl is another great language, and is great for making scripts to ease routine-tasks for a system-administrator - like going through logs or creating new log-ins from a list. Tcl/Tk is older, and fills a niche partly between Python and Perl. It includes it's own GUI-library (the Tk-part), so you can make very nice GUI-programs. All these languages are interperted, and thus slow to run but easy to program by trial-and-error with.
For HTML, CSS, PHP, ASP and JavaScript I would take a look at http://w3schools.com . http://w3.org have the standards regarding HTML and CSS. http://csszengarden.com gives ideas/examples of things you can do with CSS (and some custom graphic) to transform one and the same html-page - lots of ideas.
For Java, Oracle (the company behind Java) provides both documentation and tutorials, like http://docs.oracle.com/javase/tutorial/ .
For C++ a site like http://www.cplusplus.com/doc/tutorial/ is a good start, but there are many such sites.
"C++ for Dummies", "C for Dummies" and "Java for Dummies" are good books to start with. These are books, but it's *possible* you can also find ebook-versions - even "free-ish".