We full-timed for 16 years without making very many reservations. Since your trip is in March and April you definitely will not need reservations.
You didn't state your interests but if you enjoy the outdoors, scenic beauty and perhaps some light hiking, definitely consider staying in public parks - national, national forests, state parks and even city and county parks. You would enjoy it much better than the KOA types, plus, it will be cheaper.
Benchmark puts out a terrific atlas for each western state. You can find them online or sometimes in book stores or even Costco. They have so much detail in them with easy-to-read maps of side roads and the public parks and that's where you'll find the beauty - not on the interstates.
Also, don't try to travel a lot of hours. A good plan is around 200-300 miles max and even less in prime areas. Pull into your campground early afternoon and you'll still have time to do a little siteseeing, shopping or just relaxing.
You'll have a great trip and I predict you'll go for more at a later time!