Are you planning to change your domicile when you hit the road.. or rather, what will be your permanent address once you hand over the keys to your current home?
We went with South Dakota for ours, and for our business pursuits we did a quick partnership filing with the state and IRS so that we can do things like open a banking account in the company name and eventually get health insurance together. It was very easy and done entirely online, and cost $10 to set up. It's been a lot easier to for us to pick up random gigs as a business with a EIN.
If we should ever expand and get into business endeavours that carry more potential personal liability, we'll likely incorporate as an S-Corp or LLC to protect ourselves more.
Otherwise, nothing wrong with going sole propieter. As long as you use your real name in any business transactions, most states don't require any other filing to conduct business as yourself. But definitely check your domiciled state's regulations on that, and potentially even the state that you're conducting business in.
We can talk more about this next week over dinner if you like :)