Initially paying for the actual visa i.e. when you go the Embassy, handover your application along with your expert certificate, letter of invitation and processing fee (probably closer $100 depending on where you are) is common place. As the previous poster pointed out you should then be reimbursed for this amount after a few months of working at the school.

However, it seems as though this school is asking you to send them money in order for them to go through the whole process at their end of getting the various documents. NEVER SEND A SCHOOL MONEY TO SECURE A POSITION! How do you know that the school even exists and/or is capable of getting you a z-visa? You may end sending them money only to never hear from them again. If this is not a scam then the school has done a good job of making it sound like one!

At least you've done the right thing in regards asking and in regards applying to multiple positions. There are so many schools out there in need of foreign teachers that you can always shop around for a better deal and you should certainly not take a position which places the financial risk upon you as opposed to the school.