By the time you finish your trip you'll be pros!!
Seriously, I believe you have a 24' RV which should not give you any problems on the western roads. We're from Michigan so they were new to us, too..but now we love them.
When you begin entering the western states of Colorado, New Mexico, Arizona or even western Texas, it's not going to be climbing continuous mountains all at once. It will be gradual for you and when you do encounter a bigger uphill or downhill you'll be ready. Just relax and know that you CAN do it, as many RVers do. You just can't avoid them. If you want to travel to the national parks in the west you will not have flat roads to get there. You'll be just fine.
By the way, we were definitely flatlanders but now we now BOTH drive our 40' motorhome in the mountains.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel