If you want to learn chinese a school is gonna help you get you a visa no problem. They want your money, money, money and your foreign face to make their campus more "international."
All schools, if they have a program for foreigners to study chinese, will have their own procedures and policies over how/when etc. In most cases I think you have to apply, be accepted, pay tuition and the last step is getting your visa. It's because if you don't pay then they are not sure you are definitely coming. As long as it is a reputable school, they should have a tuition refund policy that you should check out before forking over your cash, but you will probably have to pay most, if not all, up front.
You might be nervous because getting a Z visa is harder and more complicated, and you've been reading about that. But for the most part student visas are much easier to get. Even in america my chinese friends have no problem getting a student visa, but when the same people want to go back later to travel, or to get a job, it gets trickier. So don't worry and let the school deal with most of it for you. After all, you ARE paying them.