First ever RV trip

The campgrounds is a biggy. The may be hard to find (already booked up) that time of year. You should try to line them up now cause you may have to call around to several to find one with availability. And to do that, you’ll have to finalize your stops and how long you’re staying so you know what days to book where.

So I’m a little fuzzy on your plans. You’re going to drive to one of the stops, do some sighting seeing, and eventually stop for the night where? At a campground? Big box store parking lot? Other? Do you plan on having electricity when you stop? Plug into an outlet? Generator? Other? Planning on having water for showers? etc? Need a dump station to empty tanks? 
Are you going to need heat. Air conditioning? A microwave? Are you cooking meals or eating out? Do you know how big a RV stove is? Does it have an oven?

How many suitcases you planning on taking per person? Is there enough storage? 

Five in a Class C is going to be pretty cozy, but doable for a week. You’ll have about 1 to 1-1/2 days at each stop for sightseeing, eating, showering, etc. Is that enough time for you?

Offhand, I think the learning curve on Rving in a class C has the potential to bite you in the butt big time. You don’t know what you don’t know. You may need to get some experienced person that knows about travel in a Class C to sit down with you for a few hours and put a real plan together. There are some really big potential pot holes in your road.