Wow, what a great trip! And kind of a clothing challenge. Its apt to be hotvery hotin places. During the summer months the rims top out at 80 or so, but down in the canyon it can reach 120 for daytime highs. And theres a good chance of a thunderstorm or four or five.
So my kit would include things that are comfortable in hot weather and that dry fast (from either sweat or dunks on the Colorado or from thunderstorms). My first choice for a shirt is anything made with Patagonia Capilene 1, a very light, polyester-based fabric that is an ideal by-itself layer in hot weather, and a great base layer if it cools off. The womens T is $36, and it comes in white, which could be handy.
Add to that an Icebreaker Bodybit 150 L/S Atlas Zip ($65). Its a merino wool piece, very comfortable across a wide temp range, perfect for a base layer on cooler evenings.
I might pack some cotton, but only to wear in the evening or when youre done hiking for the day, otherwise it just gets too wet when sweaty, and doesnt dry well.
For shorts, perhaps the Royal Robbins Backcountry Short ($45). Theyre made with a light, fast-drying Supplex nylon, and are designed for hiking, with a gusset for extra mobility and pockets for small essentials. It depends on the look you want, but a pair of tights for under the shorts when gets cooler would be fine. Patagonias Capilene 1 bottoms are $36 and would make a nice match with the tops.
To sort of round out the basic clothing set, The North Faces Salathe Jacket ($79) is a light fleece piece, trimly cut, thats not too warm. For those occasional desert showers, the Isis Torrent Rain Jacket ($129) packs down well, has good breathability, and will keep you dry.