There are several threads here that have done the kind of trip you plan, so first try the search box at the top of this page to see what others have done.

Decide on what kind of lodging you need and make reservations now as even camp grounds may be booked already.

Get a good map or go to one of the map sites like googlemaps or mapquest and try some routes using where you fly in to and then the add a destination to go from place to place.

Compare cost of rv rental to auto/tent and/or motel/hotel and be sure to consider the cost of fuel and limitations on miles.

You probably won't have time to visit everything on your list and some of your sites make me wonder why like why Chimney Rock and not Mesa Verde?

Get a bit more firm a plan and come back with specific questions.

A couple of things come to mind right off the bat. Skip 4 corners, it is an outlier on your trip and there is a fee to get in and see a bronze plate in the ground.

Tenting vs RV: as tempting as an RV may sound, they are a pain to drive around in some of the parks, Yellowstone in particular. You will also spend a significant amount more money on gas.

Badlands and Jewel cave are also way out of the way.

These are the ones on you list I would emphasize: Yellowstone, Lake Powell, Grand Canyon, Zion, Bryce, Moab, Monument Valley. To this I would add Grand Teton, Yosemite, and Sequoia-Kings Canyon.

HTtY

Tenting might be cheaper. Stores like Big5 Sports or Sporting Authority, or K-Mart have cheap equipment that could be donate to Goodwill at the end of the trip. By the equipment in SLC and drop it off there at the end of the trip. A tent can be had for $35, sleeping bags (particularly for summertime usage) for less, etc.

For tenting, the obvious campgrounds are National Parks. However, National Forest campgrounds are less expensive and often less crowded. BLM campgrounds are often free. I use a book of campgrounds in the West which lists all the public and private campgrounds available; unfortunately it is 20+ years old and has never been reprinted. For the most part it is still valid.

I would decide to either stick to the more northern parks (Yellowstone, Grand Teeons, Badlands, Rocky Mountain National Park, Dinosaur national Monument, and maybe dip down to southern Colorado for Mesa Verde and then go back to SLC via Arches) or decide to do the National Parks and Monuments of southern Utah, Arizona and New Mexico (adding perhaps Mesa Verde in the mix).

To whet your appetite:

http://www.flickr.com/photos/mksfca/collections/72157624514560099/

correction: Buy the equipment in SLC.

You can also rent tents, stoves, etc from REI. There equipment is far superior to "cheap stuff". It is far more expensive too, so renting is an option.