IANADL (I am not a Dutch lawyer), but if we glance at the official terms applying to all rental contracts in the Netherlands (following from the law, translated into English; there's also the dutch original) - it is not decreed that the rent be paid on a monthly basis. So, theoretically, it could be weekly, or by-monthly, or yearly; and you could agree to pay at the beginning of the period, sometime into it, or at the end of it. Still, the contracts I had been offered were all "pay once per month at the beginning of the month".
About the "extra one month" - you should separate a realtor ("makelaar")'s commission and a deposit. The first kind you pay and forfeit, the second one you pay and get back when the contract is over - assuming you don't own the landlord for anything. The height of the deposit can, unfortunately, be higher than a month's rent even when you can present proof of employment: Mine was two months' rent, but I re-negotiated that after a year and brought it down to one month's rent.
Finally, and perhaps most importantly, A point in Gala's otherwise useful answer appears to be incorrect: In section 19 of the general terms it says very clearly that a tenant can terminate the rental agreement by giving notice of somewhere between 1 and 3 months in advance; so at worst, no more than 3 months in advance can be required; and AFAICT this is relevant for the first year as well.