RV travel is not especially inexpensive. RV upkeep can be a bit spendy and/or time consuming; less money and more time the more you do yourself. I've generally found that travel with my motorhome is at best a wash compared with driving a car and staying in motels and eating in (not fancy) restaurants; admittedly I do have a fairly fuel efficient car. If spending a good length of time at a destination the motorhome does better than if only traveling for a quick trip. The overall experience is different, of course, so it's not really
a pure financial decision one way or the other often.
For the motorhome option, if you're traveling mainly to visit relatives and friends (who presumably have one or more vehicles), you could perhaps get by without towing another vehicle without too much difficulty. It's not too hard to stop for groceries and such along the way with a motorhome. It's a bigger pain to break camp and pack things up to go out for dinner one night while staying at a campground. Bicycles are sometimes a reasonable transportation alternative to a car or van, and less of a pain to carry with you (though I'm not aware offhand of any six bike racks suited for use on an RV; four bike racks do exist, the Yakima RoadTrip for one example).
For a travel trailer, a full size van can make a quite fine tow vehicle. I would not limit it to just Chevy/GMC vans; to me, the Nissan NV looks like a very nice possibility, and appears to have more comfortable seating than the Chevy or Ford E series vans (perhaps on par with the Ford Transits). I haven't done a thorough study on the matter, though; that's just first impressions.
A decent sized popup trailer might be another possibility, maybe in combination with a tent. They're easily more comfortable than a plain tent, but doesn't require a lot of tow vehicle and is comparatively inexpensive to maintain.
If you have time available, there are some good deals to be had traveling by rail, particularly with the multi-day USA rail passes. For under $500 a person (for the 15 day, 8 segment one) you can go coast to coast and back. Unfortunately, the trains don't go very close to Boise....