The teaching agency may overcharge what an agent would charge, and as it’s first time application it’s always harder. If the school is directly involved it maybe cheaper.
Until you have the work permit completed and in your hand, your not allowed to work. It takes 2-4 weeks to get a work permit, you can apply for it before you start the job. They’re probably gonna deduct the cost of work permit at an extortionate rate, I’d suggest contacting a visa agent that can organize this for you. Price is about 15k for wp application using an agent.