Luggage and bags:
El avelino or Siglo xx
Clothing/Shoes/Weather Gear: n terms of Arequipa's weather, I think it is perfect. Dry climate, if you venture out of the valley you would think you have reached the Sahara desert. The city itself, due to its high altitude-2,380 meters M (7,740 feet FT) during the day time the intense sun can make it seem like it is 80 degrees, but in the shade a nice cool breeze can cool one off really quickly. It can get a bit chilly at night, especially during the winter months of June-August, but even the coldness is not very extreme. The most I have seen it go down has been 30 degrees. So, for practical purposes bring a pair of shorts, t-shirt, sweater, jeans, sandals and shoes/hiking shoes. A hat and sun block is also a must. During the day you can wear shorts, t-shirt and sandals, and at night jeans, long sleeve shirt, sweater and even a wool/alpaca hat during the winter months (June-August).
Toiletries and Medical Supplies: You can find everything you need in Arequipa. If it's toiletries you are after try pharmacies or local mercados such as "El avelino" of "Siglo XX". These places have are flea market type infrastructure, vendor after vendor except all they sell is new. You can haggle all prices in these places and because they do not pay taxes you will find imported things half the price as you will see them in stores. Most things are from China, so if it's too cheap to be good, it probably isn't that great. It's a great place to get gear you may need on hikes, or batteries, or toiletries, etc.
Camping/Beach/Outdoor Gear: Go to "el avelino" to buy anything and all things. Go during the day and ask a secure taxi to take you there (this place is located near the bus terminal). It's not dangerous just be careful of pickpockets. There is a place near el centro where the old jail used to be that is just like "el avelino" and it's called "Siglo XX" [veinte]. You can walk here. Ask your hotel staff to give you directions. Or you can take a cab from el centro for about 3-4 soles.
Always bring a jacket with you, or something to cover yourself, because sunny or grey, the air is dry and cold. Also good hiking boots, or at least comfortable for walking.
If coming for the nordic areas, the coldness will be ridiculous for you, so disregard this message :-)
Toiletries and Medical Supplies: There are several drugstores in Arequipa that sells anything at a good price. Also bring sunscreen and balms for your skin and lips (because the weather is really dry and some white skins will tend to get scamous and drier).
Miscellaneous: Arequipa is a cheap city, and if you forget something, you'd probably find another similar in the markets or drugstore at a reasonable price.
With its sunny arid climate, you can finally enjoy walking around in shorts and sandals if you have them. But it's not that low in altitude so carry a pullover for when the sun goes down.
Toiletries and Medical Supplies: Sunblock, I did say sunny!
Photo Equipment: Make sure you bring lots of film, there is so much to take photos of in this marvelous city. A wide angle is an essential in taking photos of buildings as you are often closer than you want to be and a circular polarizer helps reduce the glare of the high Andean sun.
Miscellaneous: D's a great person to travel with, she likes taking photos as much as me. :)