First and foremost, get a lawyer. You don't have to have any money. The lawyer can build it into the divorce agreement that your ex will pay the lawyer fees. You need a lawyer for divorce, child support and custody issues. I believe most divorce lawyers handle all of that.
Since there's no court order in place, you should be able to claim your son full-time. As a single mother with no immediate income, you will qualify for low income housing. You will also qualify for food stamps, WIC (if your child is under 5), and Medicaid. You will still have to pay any utility and phone bills. Some companies will work with you, some won't.
You need to go and file NOW! If your soon to be ex husband files first, you're up a creek with out a paddle. You can't both claim your son for benefits. And you can't split his benefits, even if you have joint custody.
Good luck!