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Purchasing a van really is a non-starter for a trip like this. Unlike Australia, It is quite difficult for a non-resident visitor to purchase, license, and insure a vehicle in the US. It also generally isn't cost effective for a trip that's only a month long.
That means renting, and for that, doing a loop trip where you start and finish in the same spot will generally save you quite a bit of money.
There are not many places that rent camper vans in the US - escape is one of the few options, but I suspect that's what you were looking at when seeing a $3000+ quote.
Beyond that, if you really want a van, looking to rent a minivan from a regular rental car company is probably your only/best option. You should be able to do that for about $1000 a month. However, keep in mind, you still need to think about campground fees, and if you're planning to focus a lot of your time on cities, safe and legal parking overnight is going to be an issue.
Renting a regular car and staying in cheap hotels, hostels, and airbnb type places probably will be the cheapest route, and if you're thinking of focusing most of your time on cities, then it's probably the best option. You could additionally look at getting a cheap tent to do some camping when exploring non-urban areas.