I have several sources of good peaches in my area and have been playing around with them in beer and wine for about 10+ years.
Some observations:
-Freezing the peaches after cutting them in half seems to be the best way to handle them. After cutting the peaches and removing the pit, I place them in bags like you would use for BIAB brewing, then in a bucket and into the chest freezer for a few weeks. Or longer if I'm too busy for brewing.
-Peaches contain more acidity than most people think. Once the sugar ferments out, the remaining flavor is really tart. There are many varieties of peaches. each with a different sugar/acidity ratio, so you have to play around with what you can get. Find out what varieties your local growers have and look them up on google so you can find out which ones have less acidity.
-Most peaches are picked green. If allowed to ripen on the tree, they would be mush by the time they get to the store. Try to get tree ripened fruit from small growers or someone with a backyard tree. A note about backyard peach trees, they require lots of spraying and care to get a crop. An old farm near me has some overgrown peach trees that have peaches with absolutely no spray, but that is rare.
-Blemished peaches are generally worthless to growers, always ask of they have any blemished fruit. You can usually get them really cheap.
So to the OP's original question, any beer that would benefit from a little tartness would be a good candidate for peaches.
Peach flavor is very delicate, so add the beer to the peaches in secondary. Note that peaches are 85-90% water, so take that into account with your beer gravity and volume.
Some hops supposedly have a tree fruit/peach flavor note, maybe try something like that.
My most recent experiment with peaches was to add a high gravity wheat wine to about 4 lbs/gallon peaches in secondary. The water in the peaches diluted the alcohol more than I was expecting and the peach sweetness fermented away, leaving a tart 8-9% peach/wheat beer which is OK, but not what I was trying to achieve.