We didn't have a lot of money growing up so I took lessons at the "cheap" stables. I ended up babysitting, mucking out, feed, ect, ect in order to ride more. It taught me SOOO much, and gave me a good work ethic. You will get worked until you reach breaking point, they will take full advantage of your desire to be around horses and you probably will get little thanks for it - BUT you would learn more working on the ground than most will learn in the once a week lesson.
If you find a place willing to let you work in exchange, it could be a great stepping stone for you - in time it will also look good on a resume and show that you have drive, are a good worker and you'll have a reference long before most other kids.
Best of luck :)
Stop for a minute, open your mind, learn. You may not agree with what I say, I may not agree with what you say but we will both learn something new.