My advice? Don't pour your savings into something like that. What Growing Green said, getting out there and even just showing up, to clubs, meetups, etc, is a great way to break into the industry. I've seen it happen.
I spent most of my teenage years on programming forums, and at the end of it, I was getting cold calls from potential employers somewhat regularly because I was known to be a capable and friendly guy among the community. The field is getting a bit more crowded now-a-days, but the need is definitely still there. Employers are dying to hire someone with architecture skills, someone who specializes in a particular field, or someone who has a track record of producing cool shit.
I remember meeting a guy who coded an app that rendered a Julia set fractal on an ipad, with the fractal params set by the accelerometer. He would go around showing it to people and it was so immediately interesting, tangible, and cool looking, that I still remember him even though I only met him once for like 5 minutes. Something like that could be created in about 15 minutes if you know where to look.
The clincher, for me, was way back when I was very young, and I
Learned How To Learn programming. This may have been the most important moment of my life. I was playing around with the Unity Game Engine when it was in beta, and I reached "escape velocity" with programming. It was centered around one key command: the Unity developers had the genius foresight to integrate their API documentation with the custom-built text-editor that they were shipping at the time. It was a basic thing with no options and rudimentary syntax highlighting, but you could select any word or phrase in code, press ⌘-; and it would instantly spawn a browser window with the top hit for that phrase in the documentation. Forgive me for swearing, but it was a fucking miracle. Hypertext became like hyper space in starwars, and I blasted forward through a seemingly infinite maze of jargon, standards, concepts, and hidden gems at breakneck speed. Even though
I could at least look up every little thing and get some context or a basic explanation. I had learned how to learn. The code I could copy and paste from others wasn't mystical anymore, it was something I could fact check, index, examine, and explore.
I'm sure that the same thing applies in other places, I did the same thing a few years later with w3schools for HTML, CSS, and JavaScript. There are tons of free resources today that blow w3schools out of the water. Even if all you can do is manage markup in a web page and do some basic JS, there will still be a huge market that is dying to hire you. Media companies. Medical companies. Logistics companies. Ecommerce. Stuff you wouldn't expect. You just have to get out there, find it, and make yourself known.
It definitely can't hurt to know your stuff, and it definitely can't hurt to produce something neat and original, but even just getting out there and meeting people will work wonders.