I started programming when I was 14, with the hopes of one day working in the games industry. I started with basic and quickly(around half a year later) moved onto C++. I'm currently in the last year of my comp science degree and feel pretty confident with my abilities and familiarity with quite a few languages. So here's my advice:
Ignore the language wars and ignore the discussions on which languages are good or bad for games etc., just pick one and start. Experiment with different learning materials, I couldn't learn from websites(alt tabbing between browsers and IDE slowed me down far too much; though this was before widescreens), so I invested in some books and ended up learning much quicker.
Concentrate on general programming concepts: statements, variables, operators, memory, conditionals, loop structures, common algorithms and so on. These exist in practically every language and are far more important upfront than the nooks and crannies of any individual language. The goal of your first year or two is to learn the basics that apply to all programming, this is why it doesn't matter if your starting language is used in your desired field or not.
When you pick a language, pick one with a syntax you like and one which a good IDE and debugger, they'll make your learning experience much better, and allow you to catch and understand your errors fairly quickly. The languages that work with visual studio are a safe bet(and the ide express editions are free). Learn to use your debugger fairly early on, as soon as your code starts taking up more than a page or two; It's an invaluable tool.
Scripting languages are just as good for this as compiled languages. You can learn a lot of the important concepts through scripting. When my little brother asked me to start teaching him programming I put him to work scripting Garry's Mod addons in Lua(since he loves Gmod). Any game that uses scripting can be a great learning tool.
Lastly, don't start a non-trivial project unless you're happy to see that project fail, it'll be years before you have the knowledge to make anything that will be particularly impressive to other people. Don't let this discourage you, just keep it in mind so you don't burn yourself out with problems that you're not ready to face.
I found it useful to keep the sourcecode for Homeworld laying around. I loved that game and was psyched to understand how it worked. When I first got the code I realised I barely understood anything(it was kind of off putting TBH), but as I revisited it over the years, I found it amazing to compare how much of it I could understand compared to when I first started reading it. Something like this can be useful to help remind you how far you've progressed, so you don't trick yourself into feeling like you're not getting anywhere.
I hope this turns out useful for you OP, of for anyone else for that matter. Feel free to PM me if you have any questions.