The rule of thumb I've been told about laying refrigerators down, is that they need to stand upright again for at least the same amount of time as they were laid over before you can plug them in. As Debbie said, it's because the liquid freon can flow to places it can't usually, and then you risk the compressor running dry, which damages it. I wouldn't be concerned at all about laying a fridge down for transport from point A to home. Just let it sit for a while before you plug it in.
Definitely borrow an appliance dolly if you can, or at the very least a good hand truck. And also borrow a strong friend, lol. Teamwork is really great for getting appliance up or down stairs, and around tight corners and doorways. Also, some moving blankets or large sheets of cardboard are nice for reducing friction when sliding it in/out of the van.