Barb, Bard, Druid, Fighter are all pretty basic choices for the setting you describe. Sorcerer takes the main place of traditional Wizard. Oracle and Witch seem like a pretty good fit as well. Arcanist I was iffy on, but it makes sense for the almost hermit type wizard. Focusing on figuring magic and the way it works. Brawler due to lack of monk. Hunter fits along with Ranger/Druid in the naturalist setting. Shaman is a tradition lost world kind of trope. Slayer because more martial classes, right? Warpriest would take the place of traditional clerics. I imagine that whatever deity worship is left is focused around the more war-like gods, and warpriest fits that bill best. The rest are all of the occult classes. I purposely left Medium out, because I personally hate it.
Really you could make an argument for just about any class though. I honestly like the idea of Gunslinger in that sort of setting, but only with the newly emerging guns. Sort of reclaiming ruins of the past.