Best of luck to you - you should consider yourself very lucky to have landed a job straightaway, of course this is the time of year when most students enrol and most courses are activated. Beware any pitfalls - read the contract carefully, remember YOU are the only one looking out for yourself.
As to dates of pay, it varies greatly between employers. Is the pay date stated in the contract? Ask for it in writing! some workers are paid 27th of the month, some end of the month, some mid-following month, some 3 months later! There's no harm in checking and you'll be able to organise your finances better if you know when to expect pay. After the first month - you'll know!
An indication of whether it's a good school to work with is if any of the other teachers have stayed on year after year ...
Hope this helps,