It really does depend on what you want to do in the end... you don't want to spend years on objective C only to find when you're done that it's not what you need. An exaggerated example, but you get the idea.
First, Objective C is an EXTENSION of C. So to learn objective C you will need to know C to an extent. If you don't want to do a bunch of extensive C learning, just get the "becomeanxcoder" book at cocoalab.com. It's a free pdf tutorial that will take you from a "noob" with no experience to a beginner cocoa/objective C programmer. It will teach you enough C and general programming knowledge, and will get you started with objective C and cocoa.
I don't have a very wide knowledgebase when it comes to what language is for what, but I know a bit.
BASIC is BAD BAD BAD BAD BAD!!! Do not learn BASIC. You will pick up bad habits, and it's just naturally different from what your goal should be in any language.
Java I believe can be used cross platform, but I've heard that involves some complications and is naturally a painful language. Can someone correct me if I'm wrong?
C is pretty much a must, at least to an extent. It's the most common, most base language to learn. A lot of languages are based on it or are like it, and learning it will teach you a lot of general programming things.
Objective C is for... pretty much anything. I know people say C++ is what you want for games, but as far as I can tell so far Obj-C is fine for games as well and I'm going to give it a shot.
C++ Everyone tells me is a hard language, a weird language, and a bad one unless you're going to be very serious about learning. Either you get it or you don't is what I'm understanding. I also keep hearing that it's the best language for games of any sort.
You could also learn flash, but I wouldn't do that personally. It's a common thing, and it'll run for anyone who has a flash player but it's very expensive to get into and the apps aren't very professional looking.
Finally, there's the whole internet "programming". Personally I don't think HTML really counts as a programming language, but when you put it together with php and all those things so that you can make great websites, interactive objects, and even online apps, THEN you've got sometihng there.
There's also ruby and perl, c#, unity3D, python and other scripting languages, and a million other unknown languages and variations of languages.