I might be the only downer here, but I think this is a horrible idea. You should pursue a stable job as well and work on websites on your free time. Should your websites take off and you feel that they will bring in enough money for the long haul, then you could leave your stable job.
Pretty sure most of us are self-taught. Pick a language, add tutorial to the end of it, and type it in to Google. You won't need classes as everything is out there, but some people learn easier in a group environment with a teacher.