If you're going to rent a minivan, you might as well rent something from Budget or get the Home Depot truck. You'll also want that dolly if you're doing it yourself.
The deal with the minivan is probably the clearance but also that you can't walk into it with the dolly like you can with the open-bed truck or a large space that you'd get in the Budget truck. However, if you're buying a new washer and dryer and they're still in the box, it'll be easy to lay them down and slide them into a minivan. If you're willing to take two trips, I don't think it'll be so bad.
I moved a used washer and dryer using a dolly and the smallest truck that Budget Truck Rental has. The truck doesn't have a ramp, so the guy I bought it from helped push them into the box. He asked how I'd get them out when I got home, and I suggested that gravity would be my ally. He laughed, but it worked out fine with the sliders on the back of the dolly.
If you're interested in the Budget Truck rental (much better than UHaul), Google the words "budget truck" and click on that 15% off link right there at the top of the page.