Since you're willing to work as a web designer, I'll list you some of the languages that a web page may contain:
- HTML (Must know to start a web page).
- CSS (For styling a web page and give it some good look )
- PHP (For coding some functions that are able to Connect to databases, edit, add, delete any contect and more you'll know once you get into it).
- ASP.NET (Can handle with all Microsoft Windows Servers, if you're not willing to use PHP for that, it can be more stable when using it as a web application, also it can help you alot when dealing with MSSQL Servers it may force you to learn another .NET language for the code files such as C#).
- HTML5 (A new web application's language, it's a whole new world of web applications "http://cuttherope.ie" --> an example).
And you are free to choose from one of these