For general purpose programming learn C and once you understand the syntax upgrade to C++. For webby things I'd choose Ruby (including Rails), but PHP is good too and easy to learn/use. Also take a look at Javascript. Sadly, to make best use of the Webby languages, you should also learn SQL. I think that is 3-5 to learn, sorry.
What's with all these programming languages? I've been advised to learn a couple, but I don't know what to start with. Which are the easiest, and what exactly do they enable you to do?
You need to start one by one. C would be better choice for first. There are many programming languages, to choose one you need to understand their pits and falls over each other.