Canning peaches season is just beginning and stretches till the end of September.
A regular peach variety is classified as a "Clingstone" because the flesh sticks to the stone (pit).
A canning peach is called "Freestone" or "Clingfree", which means the pit and skin comes cleanly away from the flesh. If the flesh sticks to the skin when you're trying to remove the skin these varieties are called "Semi-Freestone". Less desirable because you will lose some of the fruit when you're canning.
I don't recommend ever buying freestone peaches in supermarkets because the fruit is picked too early and won't ripen. Normally the best 10% of the crop is shipped to Farmer's Markets where they have better handling methods. The rest of the fruit which has been picked green and unripe is washed, scrubbed, and packed for supermarkets. The fruit tastes horrible and if you do choose to buy it, only a small percentage will ever become ripe enough to can. Remember grocery chains demand hard fruit so it will have a few days shelf-life in their stores.
I have a lot of experience handling canning peaches and sold hundreds of thousands of boxes.
When you're buying peaches for canning, make sure the fruit doesn't have green shoulders. These will not ripen period. Old varieties of peaches have a green tinge, this is only true if they have been picked immature. They should be yellow in color not green. Stay away from green peaches.
Make sure they are perfectly oval or round, deformed fruit is a sign of a split stone and you will encounter difficulties trying to can the fruit. If there's a hole in the top of the peach, shake them upside down to see if bugs crawl out, insects like to crawl inside peaches.
The fruit should be firm to a little soft, press your thumb gently against the fruit. If you're buying fruit to can the same day, it can be soft but not mushy and it should smell sweet and wonderful. Ask for a sample and ask the clerk to cut a peach in half to see if the peaches truly are freestones.
Unfortunately, many hawkers in markets are not always truthful or forthcoming when it comes to telling the consumer the facts. I recommend having a regular green grocer but shop around regularly to make sure you really are getting the best quality. I have met so many dishonest hawkers in Farmer's Markets. Number #2 grade fruit is substanially cheaper and the profits are immense if a hawker can pass it off as premium fruit and premium prices.
As a retailer bad mouthing competition by "name" is never an option because it reflects poorly on yourself.
If the peaches are not quite ripe, I suggest spreading the fruit out at home at room temperature or leaving it in the box with a sheet of newspaper between the layers until it is ripe (shoulders down). You may find that to do a good job you will have to can the fruit in two batches. Usually, the fruit on the bottom layer is packed less ripe to prevent bruising. Unless you have the opportunity to pick your own fruit into the box which is best.
Riper fruit means less added sugar and more flavor. Remember the sweetest varieties have red flesh in the center and they have a fragrant aroma when they're ripe. Some of the best varieties to can are glohaven (the best), elberta, vee, "hale" varieties, "sun" varieties, and cresthaven.
Late Red haven peaches are semi-freestone so expect some waste if you prefer to can this popular variety. The Early Red Haven (less color, yellowish, smaller fruit) variety is a clingstone and I don't recommend trying to can these.
HOW TO CAN PEACHES