If you are traveling across western US and are on a budget, the best option is camping and car rental. You will need a car to access most national parks and can camp for free or pay a very small fee. In addition to national parks there are national forests, national monuments, national recreation areas, national wildlife refuges and other public lands such as Olympic Forest where you'll be able to camp.
RV vs camping RV is what I would suggest if you plan to go from one place to another. Nothing really beats the RV in my opinion because of the many options it offers. No need to worry about tent camping spots, security, etc. Plus you wont need to hire expensive car rentals.
RV's are self-contained and fully equipped with all the basics of home plus in bad weather you are completely protected, and mobile...those are the pluses of RVing. However, one big negative of camping with the RV is that RV parks are more like parking lots!