Normally, you'd start with HTML/CSS, then progress to javascript (with jquery), PHP and SQL. You'll hear a lot of talk about HTML5, HTML5 is basically HTML, CSS and Javascript all thrown in to one package
That will cover most things for web design.
It's not how long it takes to learn something, it's that you have to keep using it otherwise you forget it. I learnt how to use the bootstrap framework 6 months ago, can't remember a thing now.
C++ and C are really the daddies of programming and they cover your main software types, not really anything web related but learning it will create a great understanding of programming basics and theory. It's not easy though and you have to be extremely motivated. Throw C# into the mix as well as people often recommend this language, and you've also got microsofts web language which I believe is asp.net but I've zero experience of that.
Python, great language, easy to learn and lots of resources out there. It can be used for lots of things, including web stuff. I've used it for several things from pulling live website data to simple software. It's great for data science things. It's a good first language but the main criticism it receives is that because it's a high level language some programming concepts you would pick up with C for instance you don't learn about.
If I was you, pop over to
https://www.codecademy.com/ and have a play with their courses. Covers a lot of subjects for free and gives you a decent start, it doesn't cover a lot of things but will give you enough knowledge to be able to research things on your own. I think if you lack patience this method will give you the boost you need to decide if it's for you or not.
Ultimately, what a lot of people don't tell you is that programming isn't about the language used, it's a state of mind, how you look at problems and solutions. If you can get that way of thinking down, you will pick languages up quickly enough. Also ignore anyone that says one language is better than another, a language is a tool, you pick the right tool for the job
There is also a good thread on here you may find useful:
http://forums.overclockers.co.uk/showthread.php?t=18577095