I'd go with a 50/50 mix of dirt (if the dirt in your yard is anywhere near OK that is fine) and good compost. If you don't make your own you can buy very nice compost in bags at the Agway or large garden center. Where did you get the peach tree?

I'd likely dig a hole as deep as the root ball (check to make sure the tree itself isn't already buried in the pot too deeply) and twice as wide. I'd loosen the roots a bit, then set the tree in the hole and backfill with the soil/compost mix until the hole was about half full. Then I'd add water, and wiggle the tree around to get rid of air bubbles. Then I'd finish backfilling with the soil/compost mix, then add more water. Then I'd make a ridge a couple few inches high at a few feet away from the trunk, and fill the area inside that ridge with water. Then I'd water, um, weekly I guess since the weather's really cooling off now, until the ground gets hard.

What kind of soil do you have?
If what you have is clay do not mix anything with the clay or you will create a soil that will allow lots of water to accumulate in the soil around the roots of the tree where it will stay because the clay soil outside the planting hole will not allow that water to drain away and your tree will drown.
If you have sand for soil you can mix a lot of compost with the soil you took out of the planting hole before you put it back in and that compost will aid in keeping water around the trees roots. However, mulch well to help that too.

Here is a link that might be useful: Planting a tree

I bought the tree for $10.00 marked down from $40.00 at my local Stop and Shop (grocery store). It is in a black plastic container. Tree has a few leaves left on it. I don't have compost but i do have peat moss and leaves. Will that do? Or should I splurge on the bag of compost from the local garden center? I have mostly sandy soil with clay in some spots (the middle of the lawn is clay).
I have been trying to get info on the tree. The tags says it produces great fruit but when I look it up on the internet it says it is just ornamental. I don't care either way. If it does have edible fruit I will have to spray it.. I do not love plants that require lots of maintenance. I took out all my roses this fall for just that reason. Lovelycherry

I bought the tree for $10.00 marked down from $40.00 at my local Stop and Shop

Uh oh. Oh well, if it doesn't live you're only out ten bucks.
I don't have compost but i do have peat moss and leaves. Will that do?

Nope. Poor little Stop & Shop tree is gonna need all the help it can get. Buy a bag or two of good compost.

If it's an experiment, don't get too worked up about it. That said, a big thing like a tree needs a bit of work to get properly started, then about a year of some attention. Once established it should go for years and years with very little attention beyond a little pruning.

I wouldn't add compost to the hole, especially if you have clay soil!!

Dig a hole bigger than the roots extend. If potbopund- cut away at the outer layer of roots to stimulate new root growth. Dig a BIG hole. Plant in native soil only. Step on the soil around the root ball with all of your weight. Water, water, water. You want to wash soil into any air pockets created, as they will foster rot.

Add compost to the top. Fertilize in the spring.

pablo's happens to agree with the research at the University of Ga. Dig a wide hole sit the root ball in the middle and backfill with native dirt.

University of California recommends mulch on the surface as big as the canopy. Their work showed as much as 3 times the growth with mulch on the surface vs grass.

The tree is a Bonfire Patio Peach tree from the Virginia Berry Farm. Only gets about 5 ft, it should gtow a foot a year. I think it will be fine. Fall planting for trees is the best time. I will get the tree in the ground this morning. Lovelycherry

Forgot the other part of the UC research, they theorize that grass has a juglone effect on the trees. Which makes sense that the grass would try to keep the tree from growing and shading out the grass.

Ju´glone
n. 1. (Chem.) A yellow crystalline substance (C10H6O3) resembling quinone, extracted from green shucks of the walnut (Juglans regia); - called also nucin. Chemically, it is 5-hydroxy-1,4-naphthalenedione.

Keeps other plants from growing around it.

Thanks lovely, always appreciate specifics.
Notice they said "ju'glone effect" which suppresses growth of the trees. They did not specify why the trees did MUCH better mulched than with grass, of course I think organic matter in the form of mulch helps everything!

The accepted horticultural convention is NOT to amend individual planting holes. If necessary, amending the soil over a wide planting area can be advantageous, specially if very sandy, low organic soils but you can impact drainage and create soil interface issues that hamper root development if you amend individual plantings. And the "bathtub" aspect will most certainly come into play if doing so on heavy, clay-based soils. An organic mulch spread lightly and widely over the root zone after planting is far more preferable.

As to grass having an allelopathic effect similar to juglone, lawns/turf grasses are notorious water and nutrient hogs and will impede the establishment of young trees, outcompeting the delicate feeder roots for these items. And of course, there is always the danger of mower or string trimmer damage to young trees plunked down in the middle of a lawn, which next to improper watering is the is the number one cause of young tree fatalities.

'Bonfire' is considered an ornamental rather than fruiting peach, characterized by bright red new growth. It will occasionally produce not very tasty fruit.

I also bought a peach tree on sale from Stop & Shop dirt cheap. I'm not doing much for it.
Let me know how yours works out.