I'll do my best to give my professional opinion for your situation. I know it can be exciting to be asked to cook for a family, but I just want to hopefully give you a few things to think about before just jumping straight into being a personal chef. You may already know most all of what I'm going to bring up, but I'm just trying to help. You don't have to answer publicly, but ask yourself some questions.
Does Miami require a business license?
Does running your business in a client's home require you to be insured? (worst case scenario, you have a grease fire, throw water on it and burn their house down.)
Do you have any legal safe guards in case a member gets sick, blames your cooking and sues you?
Does your state or city require a food handlers card, ServSafe certification, or comparable proof of training?
Does your state require you to collect taxes?
I'm not trying to scare you, I'm just trying to help anyone considering the business to make sure they're covered since most people will more than likely be going into the business as a sole propreitor. If you already have a business set up incorporated or as an LLC, bonus. I'm not a lawyer, but I know there's a few hoops to jump through regardless what state you're in.
As far as pricing, it seems like you'll be doing family style cooking, that's good, your days should be shorter. It may be best for you to set up a per hour or per day rate plus groceries. It'd be best for you to do the grocery shopping because you'll know exactly what you'll need to cook your menu, and you'll ensure you're picking the best possible produce. Get a grocery store deposit before shopping or, in your client agreement, make sure you are compensated for your receipt upon job completion.
There are a number of variables to consider before settling on price, but I think a fair price for this particular service would be $100 - $175 per cook day + groceries ($500 - $875 per week). A selling point as a personal chef is the ability to personalize their menus, quantities, nutrition, etc. to suit them as a family and provide them with restaurant quality food. If they say thats too pricey, break it down for them. That's roughly 60 meals a week, you're doing their grocery shopping, cooking, and kitchen cleanup.
I know they said they like pretty much anything, but in my experience, that is rarely true. Google personal chef client questionnaire, and go over the questions with the family. Make sure allergies are part of the questions.
Hopefully I've covered a decent amount of bullet points, but there is a lot more to it than I wrote here. Things like maintaining inventory, labeling, storage, other legal forms, etc. If you haven't yet, go to Amazon.com and find a good book or two on being a personal chef. If you already have, good for you
It's a good and profitable business to get into, but it is still "a business". Good luck with your venture!