Hi, been to Upper Antelope Canyon twice, never made it down to Lower part. Was there last October. I'd google and call some of the photography tour leaders there to see what is best time to go, it changes depending on the season. Usually best time is still early morning between 8am-10am.
Must have tripod and cable release to get good shots. Better to not change lenses while in there as there is so much fine dust from the sand floating around that once you open your camera you're sure to flood it with dust.
Upper part is almost always flooded with tourists. Lower part is less busy as it is a bit harder to reach especially since you have to go down a ladder. I wouldn't carry a big camera backpack.
Have a great time.