Hello and welcome to the RTA forums !

Yes, it is a popular trip and 3 weeks would be a nice amount of time to explore along the way, but would also offer a million and one things to do. A coastal route, an inland route or taking a wide arc out to Yellowstone and Utah [as an example ] would be possible.

You do have to be of a certain age to drive in America, but at 25 you are OK and past the dreaded 'Young driver surcharge' on rental costs.

European type 'Camper vans' are rare in the US and come at a premium. The RV is more the norm in the US, but are designed more for family's and are costly for a solo, or a Couple's road trip, and both would be more expensive than a car and cheap Motels. If you started a loop trip from SF you could check out a Company called 'Lost campers' for a good value 'go between'. Starting and ending in the same location will avoid having to pay 'One way drop off fee's' as well.

Search the forums and road trip planning pages for ideas and inspiration with a good map to hand and start putting some dots on it. When you have the basics down we can help to fill in the blanks, and as new questions crop up, just ask !

Hint; Scroll to the bottom of this page and you will find 'Similar threads', and repeat as many times as you care too, enjoy the planning !