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I do not know Mr. Gatto, nor do I know if he has a flat fee structure, this is certainly something you should address with him in your consultation.
It is not necessary to take any documents with you on the first visit to a lawyer, as it is generally a short meeting lasting little more than an hour, however if you can put your hands on last year’s tax returns, a few paystubs and your bank account and retirement account balances your attorney will be better able to understand your property case.
Asset distribution depends on the type of case you are dealing with. If the matter is litigated (goes through the court system) I would estimate it will take anywhere from 6 months to 12 months before an Equitable Distribution trial will be heard. If you work things out in a non-litigated settlement (depending on the agreeability of your spouse) it can happen pretty quickly.
As for the money you spent during your initial separation period how it will be counted depends on whether or not you and your spouse reconciled after you returned home.