We went in June last year, and it was pretty darn hot, except at the GC at night. Short sleeves and breathable is the way to go, with a sweater or light jacket to layer in the evening.
You can get away with sturdy walking shoes or low hikers. A lot of people on our trip wore their lands end water shoes all the time, the trekkers like this
http://www.landsend.com/pp/TrekkerShoes~191688_253.html?bcc=y&action=order_more&sku_0=::FKH&CM_MERCH=IDX_00009__0000000917&origin=index. These were perfect for the rafting as well. The earth is very dusty & red there, so don't get brand new white shoes for this trip - everything we wore came back stained orange!
You only need to bring a travel size sunscreen. The guides carry plenty of it, along with bug spray and water. We got by with just a little face stick and used their spray for arms and legs.
Definitely sunglasses. Hats if you like to shade your face. The sun does beat down there. And I second the bandana idea. It was great for Monument Valley.
Um, other tips, hmmmm....if you've never done an
ABD, you may not know that you safely leave a bag on the bus during day trips. So you only need a little purse or camera bag, and you can have a backpack with extra jackets, batteries, etc that you have "with" you on the bus but don't need to carry all the time. You also might want to take an outfit to change into at the end of the day. We would have time on this trip to freshen up after a dusty excursion, before meeting back for dinner, and I was glad to put on something fresh. Not two outfits every day, but maybe one or two extras overall.
That's all I can think of right now. Let us know if you have other specific questions. You're going to love Southwest Splendors!