Okay, good picture you painted, but you didn't use the tools you were given. You've painted a picture of a nuclear family with two above minimum wage workers with the possibility of a working teen.
The scenario is a single, working adult on their own making minimum wage. You also chose a state that has a higher than federal minimum wage, which, btw, is $8.15.
Okay, let's start there with the extra $36 a week that higher wage gives. Step one for someone that just left home.
Finding the job. In a city, it shouldn't be difficult thanks to public transportation. Car ownership is expensive. Besides a car payment, you have gas, oil, antifreeze, brake fluid, power steering fluid, washer fluid, and the big one: Insurance. Unless you're in the know, you're better off sticking to a bicycle. You could get a moped, but you'd still have operating expenses. Including insurance.
So, while nice, as a minimum wage worker, on your own, it's either going to be public transportation, or in good weather, a bike.
Let's start with housing. As you chose Ohio, I selected Columbus as a place to live. Think you'll buy a house? Difficult on minimum wage unless you have prior savings. You could pick up an old house at tax auction, but you have a 1 year waiting period before you can evict anyone living there. If the previous owner pays the tax debt, your back to square one, although you'll be refunded the money you paid. But say you get the place. Is it liveable? How much work will you have to put into it. Could likely cost you more in the beginning.
Most people, however, don't go that route. They usually rent a place. You can rent a sleeping room for about $100 a week but you may not have kitchen privileges. Or you may habe others that like the food you bring in. Sleeping room is a stopgap, good for a week or two, but not longer. Meanwhile, I found studio apartments in Columbus starting at $400 a month. Add your deposit, first month would be $800. Cover that from your savings.
Furniture? A futon for sitting and sleeping, or a used sofa sleeper. Recommend go with the futon in a studio apartment. If your folks don't have one to take along, buy local. A good one with a good mattress will cost about $500. This is one thing you don't want to buy used. Again, that comes out of your savings. Table and chairs, dresser. That should cover it. Blankets, towels, washclothes. Your folks may provide those. Same with dishes and pots and pans. More>>>>