Most likely, whatever fruit, if any that forms from the suckers, will be of poor quality. You can try your hand at grafting into one of the suckers. It's a fun experiment and you have the ability to add several varieties of peach where you only had one. Cheap to do if you can have some scionwood from friends in the area that have a good variety growing.

Let them all go now. This February while dormant cut all but two. If both break dormancy next spring select the largest and most dominant growing and keep it and cut the other.
Let that grow for a season and line up some scion wood for the following spring. Graft it and wala...you're back in business.