There are new organic "chemical" sprays - often made by the same chemical companies that sell the more toxic stuff. You shouldn't need sprays for the figs but everything else on your list will suffer around here.

You can usually find dormant oil at any large garden center or farm store - it is not considered a chemical by most gardeners. You'll spray it in late winter before the flowers open on any fruit trees. Then there are fungicides and insecticides that you spray either right before the buds open or right when the petals start to fall off the flowers. You don't spray while the flowers are in full bloom or else you'll poison your pollinating insects (like bees). In some parts of this area you have to basically spray every 10 days until harvest. Most of the bottles have the instructions on how to mix the chemical and when to spray it - it is different for different parts of the state.

There are couple of diseases here that can ruin an orchard. Diseases that the rest of the country rarely sees so make sure any information you look up is for the south east part of the US.

Make sure you plant the most disease resistant apples you can find - I like 'Williams Pride', 'Goldrush' and 'Arkansas Black'. Even with their exceptional disease resistance they all suffer from something in my yard. The most disease resistant for me is 'Arkansas Black' but its apples don't have the flavor that the other two have.

Plums can suffer from a few different diseases than apples - but they don't need to sprayed as often. A bigger problem is bugs eating the fruit before it ripens in my yard.

Peaches grow like weeds. No matter how much you spray eventually the tree will die so be prepared to replace the tree within 10-15 years. Don't worry about buying the biggest trees in the store - they grow really fast here.

"Don't worry about buying the biggest trees in the store - they grow really fast here."
Good point. You are much better off buying a newly grafted one-year "whip" from a reputable online nursery. The trees at Lowe's have spent two years in a 2 or 3 gallon pot and are hopelessly rootbound. After transplant, they will spend a whole year recovering. I mean they will leaf out, but won't put out much new growth. If you plant a one year bare-root whip in November, it spends all winter establishing fresh roots and will take off like a rocket in Spring, far surpassing any potted fruit tree from big box stores.
And ditto on the Goldrush, an excellent apple. If you haven't had one you can find them at the Raleigh FM beginning in Sept.