Renting is a good idea, especially if you've never traveled this way before. BUT ... renting a motorhome is pricey. The most common rentals are the Class C's -- the RVs that look like a van up front with a bed over the cab.
As far as traveling by pop-up, I'd caution you that while they tow really well they're a bit time-consuming to set up, and you have to set them up pretty completely to even sleep in them. Plus, you've got to have the proper towing "package" on your car.
I think that you need to ask yourself what you feel most comfortable with. What do you plan to do as you travel? Do you want to stay in 1 place for more than 1-2 nights so you can sightsee, or are you going to drive straight through? Do you want all the comforts of home in a small package that can be left at a campground while you tootle around in your car, or do you want to tow a vehicle behind something big?
Yeah, there are lots & lots of considerations. One of the best things to do is go sit in every conceivable type of rig there is and ask every question you can think of. Buying an RV is a process that's as individual as everyone who posts here, as are our reasons for buying what we did.
Enjoy the process & keep asking questions. You'll figure out what you want eventually. Enjoy! And welcome!
Laura -- and Jed