Yeah, thats an interesting set of activities. The one thing that makes it a bit easier is that you wont be seeing any real cold weather. Cool, yes, particularly in Sedona. But not cold.
So...something like this:
Rain Jacket: On the more affordable end, Mountain Hardwears Exposure II Parka ($200), made with its proprietary Conduit fabric, is quite good. Durable, waterproof, decent breathability. If you can spend a bit more, I highly recommend the REI Shuksan ($299). Its made with eVent, a fabric that is similar to the PTFE used by "the" rainwear-fabric maker, but that undergoes a little different manufacturing process. Really breathable. And overall the Shuksan is a really nicely designed jacket.
Backpack: Id like to see if you can squeeze into something around 4,000 cubic inches of storage. Gregorys Baltoro 70 ($289) has a bit more than thatabout 4,300 cubic inchesin an easy-carrying, easy-to-pack design. Its a rugged pack that can manage a heavy load. I also like Ospreys Aether 70 ($260), which is about the same size as the Baltoro, and is just a touch lighter. Ive carried both in the past year and love them both. If you want something bigger,REIs XT 85 ($299) puts 5,200 cubic inches of capacity and cutting-edge materials into an affordable package. A lot of pack for the money. And it weighs no more than the Osprey.
Sleeping: That's a tough one. I should think for your U.S. stages, a bag rated to about 32 degrees would be fine. In Asia, you might not even need it, depending on where you are going. Marmots Arroyo ($249) is a classic, very light (1 pound, 11 ounces) down-filled bag rated to 30 degrees. Packs to the size of a cantaloupe. For something warmer, and synthetic, The North Faces Cats Meow ($159) is a classic; rated to 20 degrees, weighs a little under 3 pounds, very durable.
Tent: Probably MSRs Hubba ($280), a solo tent that weighs under three pounds and has plenty of room for you. Great breathability and good weather protection. And bug-proof. If you think you may have company, Big Agness Seedhouse 2 SL2 ($320) weighs only a little more yet has room for two. And Sierra Designs' Meteor Light 2 ($280) is a classic two-person design, but it has a little less mesh than the lighter tents, so its warmer in cool weather. Weighs about six pounds.