Homebrew is not a bad place to start though. It gets you acquainted with the console and the hardware that makes it tick.
Unfortunately, I don't have 1800USD either so I can't buy it now. The only SDK I ever got my hands on was a decommissioned xbox1 XDK. Aside from that, I've used the 360 XDK on the job once (that was fun!); just wish it would have lasted a bit longer. I could be wrong, but after reading the developer application, I assume you have to have a valid company (indie with a sole proprietorship or bigger business LLC or Corporation) since it asks you for your company name and your position in that company.
Now, if your dad buys you a PS3 licence at the age of 14 and you end up writing a popular game, that would be a jaw dropper that would make great gaming history. You'd probably end up on TV too. Don't get me wrong, I'm not saying that I don't believe you can do it, but when I look back when I was 14, I didn't have things nearly as well as you do now. There was no gamedev.net, no shaders (at least not on consumer hardware), no Visual Studio Express, depending on where you lived no career support, and virtually no support for indie devs except for Xtreme Games. If you have parents that will back you up on this, go for it. At 14, I was pretty much on my own.
Shogun.