I can't really give effective experience advice, as I was kind of already into software development when I became interested in games.
But if you think that you are interested in programming and software development outside of the realm of games, then by all means jump headfirst into it. I would recommend starting out with C on GNU/Linux, as that system is completely free (http://www.gnu.org/philosophy/free-sw.html) so you can see a tool you want to use, use it, and make changes (be they improvements or not). Most (not all) GNU/Linux distributions are also free as in zero cost. I would recommend those (I strongly recommend Linux Mint. It provides the convenience, compatibility, and mainstream-ness of Ubuntu without all of the bullshit.). C will get you far in the Linux world, and you can always just read about classes, templates, and the other new flashy stuff to say you know C++.
If you are not interested in actually interacting with computer instruction and programming, I would recommend finding an engine that roughly fits your game, and going from there. You won't have to reinvent the wheel, but you also won't get to build a sled instead. If you want to make a game, but don't want to spend all of the time making a new game, you can always just mod.