All overnight stays below the rim except for Phantom Ranch require a backcountry permit. This includes Bright Angel campground. It's very late to be planning an October hike which is the most popular month. The first day for permit applications for Oct was June 1. They are likely all booked. However they do hold back a few for walkups. The following link provides info on the GC backcountry permit process. Yes you need to provide and carry all your own camping gear. The only thing in the BA camp sites are picnic table and ammo boxes for protecting food from critters.