Suggest that you always carry a light windbreaker, even in warm weather. The winds can kick up to 50mph suddenly, and the windbreaker will help cut the dust and possibly the chilly air that can accompany the wind.
Photo Equipment: Due to the sand in the air, I suggest that you keep a UV filter lens on your camera (for those who have the old-fashioned film cameras)
Luggage and bags:
Any luggage is fine, don't go too fancy though. Have a comfortable backpack so you can carry your camera, water, mapc, etc. around.
Clothing/Shoes/Weather Gear: Baku is a windy city. Always good to bring a wind-breaker. Summers can get very humid and hot. So bring along your hat and some sun-screen (although locally available).
Toiletries and Medical Supplies: You can find just about anything in Baku, but there is no Advil or Vaseline Intensive Care. So if you're used to a particular type of medicine or toiletry, just bring it with you.
Photo Equipment: Very hard to find disposable cameras, but films and batteries are cheap and available.
Camping/Beach/Outdoor Gear: You won't really find a shop in Baku that sells this type of gear. If you're going backpacking, bring all that is necessary with you. Especially tents and all.
Miscellaneous: You can find just about anything you want/need in Baku but you may not be happy with the price or the quality. I recommend that you bring whatever it is that you think maybe useful and don't think twice.
Luggage and bags: Apples- as can be seen in this 'loaded Lada' travelling south to Baku - you can never bring too many apples!
Toiletries and Medical Supplies: You must and I mean MUST have a toilet tissue with you if planning on traveling to Azerbaijan. You are not going to regret it and it will become handy. Better safe than sorry!