Marilyn, some info on what I do...
when I buy the peaches like you're describing, I wait until this time of year (they start appearing in June and those are hopeless). My market will put the seasonal produce in huge end bins because it is plentiful and the cheapest price it will be for the year.
My method:
I select only from the top rear to reduce the possibility of other shoppers having squeezed, dropped, or abused.
I sniff at the stem end for any trace of a scent. Some will have a very faint scent, most do not. Only select the ones with a discernible scent.
Any peach that passes the first two tests will then be inspected for bruises, cuts, or any other blemishes. If the fruit is less than perfect, it will rot before it has time to ripen.
The peaches are carefully placed in multiple bags, do not pile them into one big bag, they will get bruised.
Carefully guard them throughout shopping, don't let anything rest on top of them.
Hand place them on the scale for the cashier. DO NOT let the cashier EVER touch your peaches. Remove them from the scale and safeguard them after they have been weighed. If the cashier is allowed to touch the peaches, he/she will lob them off the scale and down the belt, and your peaches will start rotting before they have a chance to ripen.
At home, place them in a single layer in a large dish and set aside for a few days to finish ripening.
After all this, you will get some fairly good fresh peaches. I just finished up my second cycle of the season and the peach I had for breakfast, that started out as a rock when I bought it, was dripping juicy sweet peach juice down my hands as I ate it. Good luck.