To put some perspective on the romanticism of all this, shorten title to 'live on the road'. I grew up going on camping 'holidays' in the UK as my father was a great romantic, the reality in the US today is a lot more regimented anywhere near surburbia.
There are trailer parks in the USA for a reason - a lot of people associate free spirited travellers as littering gypsies and in many areas you are going to be harassed by the police.
I have a friend who has a great looking vintage truck with a vintage camper shell on it with sink, cooker etc. He has long hair and he and his wife are constantly harassed when on the road. The police can be extremely unpleasant. He owns 3 houses but is used to the police calling him a down and out.
Adding to @josefresco's comments before you spend a fortune kitting out a van rent one for a month and live in it in the mild weather spring or fall to get an idea of what it's like and what you need.
Also be aware a van can get stolen with all your possessions in it. I had a 26 foot vintage airstream I was going to restore stolen, apparently any sort of mobile living space is a great target for people who live in the woods to steal and hide off road. Be realistic about what you are getting into and install excellent security.
My home area is Austin but I've traveled up the east coast a few times and through New Mexico. Many areas of CA are hard since there are a lot of NIMBY anti-homeless laws. The midwest has a ton of BLM land so it's one of the easiest places to camp, so long as you don't mind being in the middle of nowhere.
Middle of nowhere is rarely a problem I agree from my personal experiences too - it's proximity to particularly small towns with bored cops where my friend has the most problems, including just driving through. Must be a visual thing, maybe he triggers something with cops. His wife is gorgeous, maybe that is a stimulant also. Mileage may vary etc with personal experiences
