Experience is great but in three years at one place all your going to know is that one place really well. Schooling brings a broad range of experiences form many backgrounds.
Many places are very inbred with ideas and the way to do things.
There is such a plethora of techniques to do almost any thing in the kitchen that learning from only one chef can be fatal to a career. Again I feel Practical experience is is a must before schooling but schooling is still the most efficient way of gain knowledge. Do all the things that Chef Rene suggests but do go to School. I am not saying don't go to school, what I am saying don't spend your money in culinary schools before you get some experience. When you finiish with your apprentiship I suggest inmediately leave that property and start working as a cook in other places.