finding a center that will take any child who is not potty trained is about impossible out here (california), the few i know of that do won't take a newborn before 6 weeks of age and charge almost $1000.00 per month (justified by VERY HIGH liability insurance, much higher staff to child ratio, much more labor intensive), i think private homes charge 600-800 per week.
def. get a contract written with cost, how you will handle planned days off (will you still charge if they will be gone for 2 days one week), what time off you require (x number of vacation time per year with so much advance notice to the parent), call-in policy (how soon you expect them to get there if you feel they need to retrieve the child due to illness), sick policy (are you willing to provide care when the child is sick, running a fever, diareah-and are you comfortable medicating someone elses child), overtime charges (sadly, some parents will pick up late due to wanting to run errands w/o baby in tow-it can impair your ability to do planned activities, and with 4 of your own i imagine they have a few

), who will provide what (the providers here generaly require the parents to provide ALL FOOD PRODUCTS (safety when it comes to allergy detection), wipes, diapers, ointments, lotions...), and bedding (if they want the childs bedding washed in a particular product).