Camel

Then I'd recommend the tubus "cargo" model rack, in combination with a very good quality pannier. The rack and bag will likely cost you 200+$ total. You can sometimes luck out and find a good bag on e-bay/craigslist at a realy good price.

I'd recommend a smaller pannier, one which cycle tourists would normally use on a front rack. Something like an Ortlieb classic bag would suite your post requirements and have extra room. This bag also has a narrow profile, especially if not packed full. Another cost saving option would be to use a racktop trunk bag. some can be expanded to fit your size requirements as posted. Trunk bags are much cheaper than panniers, and a good quality one will stay on the rack no problems.

Mind that the rack mounting will depend on the bike having rack eyelets or not. If not then going with an Old Man Mountain rack might be better because they have work around systems for bikes w/o eyelets (and bikes running disc brakes). The work around system may not be as sturdy as direct mounting-but that's my opinion only. You can also cludge together works arounds by using hardware from your local hardware store/home depot.

CHeck out what folks have used for gear along the Great Divide Mountain Bike route, or the annual race