I have no advice on footwear. I have seen folks in quite a bit of different footwear. Most of it runs in the nature of trail shoes/runners to heavier boots, but there are all kinds of exceptions.
Two years ago, my son's Boy Scout troop had a kid go up San Jacinto in a shoe duct taped back together. This last trip, I saw one woman above High Lake on the way up NAP and after a snow field or two, and she was wearing in flip flops. I didn't say anything, but I thought she was crazy. She, on the other hand, didn't seem bothered.