The term "computer language" generally refers to a programming language; i.e., a notation for providing detailed instructions to a computer, telling it "what to do" - accept data input from one or more sources, perform various calculations or transformations upon that input, and place the results one place or another.
There are *many* such notations, or languages, for doing this. C, C++, Java, PHP, Perl, Pascal, Python, BASIC, Ruby, SQL, Modula-2, Prolog, C#, Smalltalk, COBOL, assembler, etc., etc. Many languages are particularly suited for solving problems in a given "domain", or area within the real world. Real-time digital signal processing software, for instance, may be written in a combination of C and assembler. Interacting with databases may be done in SQL, though many SQL servers provide have "APIs" (Application Programming Interfaces) that provide functions in other languages to access the SQL capabilities. Programming for the internet/web is likely to be done in languages such as Java, PHP, Perl, and Javascript, although these languages can be used in other contexts (surprisingly different contexts, actually).
Although there is no "universal" language, there are several nearly ubiquitous languages, and these include the ones you've probably already heard of. [Assembler languages are more computer-friendly than human-friendly, and are essentially mnemonics for machine language instructions (patterns of 1's and 0's). I doubt you'll want to go there.]
You mentioned Unix and Linux. These are not languages, but "operating systems", which provide a sort of glue between "application programs" and the hardware. That is, the operating system performs various services on behalf of application programs, like storing data to and retrieving data from disk drives, or sending data across a network port, accepting your keyboard and mouse input, and displaying output to the screen. Applications programs are programs like spreadsheet software, a text editor, a cost-analysis program, a video game, and so forth. Unix, Linux, Windows and OS X are also operating systems. Strictly speaking, Linux is an Operating System kernel, but it's okay to use the term more loosely to refer to the whole OS.
There are "shell languages" for these operating systems that allow you to provide a series of instructions to a "command interpreter"; the operating system performs those instructions on your behalf as if you'd typed them in yourself. Perhaps that is what you were referring to when you mentioned Unix and Linux. (bash, sh, csh are common command interpreter/scripting languages for Unix and Unix-like operating systems.)
Where to start? In my opinion, a language that derives much of its syntax from C will do you well. C, C++, and PHP are some of my favorites. Object-oriented languages are more and more important as time goes by, so C++, Java, Ruby, PHP (especially PHP5), Python or Delphi would be good choices. Your target operating system might be a factor, too. Java is a cross-platform language, C++ is available nearly everywhere, any of the Visual Studio languages would be good for Windows-based software, and they have great built-in help systems and tutorials. For the application domain you're talking about, I think C++ is not a bad place to begin. It's hard to pick a bad one, though.
People tend to get into religious wars over what language is truly "best". The best language is the one that you wield most successfully to solve the kinds of problems you are trying to solve, in the environment in which you are trying to solve them. A bit of trial and error is inevitable. Get something free, for learning. I'm a PHP consultant, writing desktop and web-based solutions in it, so I'm bound to be partial to it these days, and there are number of very good introductory books for it, but don't let anyone goad you into this or that language because they think it the best. Talk to providers of the kind of software you're interested in writing and see what they seem to use. Look for job postings for that kind of software and see what language you see required the most.
Best wishes on your programming endeavors.