You shouldn't really worry about this too much. Too many small channels get clouded with these fantasies of partnerships, that will somehow help them boost their channel, or make a lot of money from. You'll be much happier, if you don't worry about partnership, or go searching for it and let it come to you, when the time is right.
But to answer your questions:
when should I start the monetization process? As soon as you're partnered. If you're a gaming channel, don't monitize your videos at all.
And how much money will I make? Not much, don't expect to be earning bagfuls at the start. Most of the time you won't even earn enough to go and buy a slice of pizza.
Is it different per contract? Yep.
Hope this post helps my man!