As for what to wear, it's a classic layering situation. You'll need shorts and a T-shirt for warm weather (REI Sahara shorts: $34; www.rei.com; Layers CoolMax T-shirt: $32; www.layers-outdoor.com). When it cools a bit, a set of light long underwear goes on (Duofold Varitherm long-sleeve tops and bottom: $20 for the set; www.duofold.com). Cooler yet, layer up with pants and a fleece jacket (Ex Officio Amphi Pants: $59; www.exofficio.com; and L.L. Bean Super 200 Trailwind Fleece Jacket: $69; www.llbean.com). And if it rains—yes, it rains in Arizona—then a waterproof layer (Marmot PreCip jacket and pants: $100 and $70; www.marmot.com). Toss in some gloves plus a couple of hats, and you'll be astonished at the range of climatic conditions that setup will see you through.
For a sleeping bag, I think one rated to around freezing or a little above would be fine. An example: Lafuma's Warm'n Lite One Kilo ($159; www.lafuma.fr). For shelter, try the Big Agnes Seedhouse 1 ($169; www.bigagnes.com), if indeed it's just you along for the trip. Throw in a Jetboil Personal Cooking System ($80; www.jetboil.com) and you're all set. Stuff it all in a Kelty Haiku 3000 pack ($160; www.kelty.com), load up the car, hit the trailhead, and away you go.
Now I know this bill will be a little stiff if you're buying all this from scratch. But you'll get years of use out of it all, and it will serve you well for when you decide to keep going and hike all the way to Canada on the Continental Divide Trail.
Now, about that water issue...
Read reviews of the Jetboil stove (2004 Gear of the Year) and more essential through-hiking gear in Outside's 2004 Buyer's Guide. For more on the Arizona Trail, please visit Outside Online's partner site, GORP.com, and "Sand, Snow and Solitude: Traversing the Arizona Trail".