I once drove 100+ miles with one of the standup models in the back of an 80's nissan frontier with the cab laying flat on it's back in the bed. It made the trip just fine other than a few scratches on the back. I'd say you have nothing to worry about if it'll fit in your minivan and you have two people to lift it, all that metal and the monitor can be heavy. I would recommend removing the marquee holder first and securing anything inside the cab that isn't bolted down. You might need a security bit. Whatever you do don't damage that marquee holder!! They are a impossible to find. At least that was the case 8 years ago.
Not really on the back. Its just a plastic shroud with 6 bolts holding it and can break from the weight of the monitor transporting. Side or monitor down properly cushioned is the best IMO.
Don't put the Naomi Universal/Net City/New Net City on their backs! Like RepX said, it's just a hard plastic shroud and if it breaks, it might damage the monitor.
I have transported on it's side before and it was fine. So I suggest on it's side. And they are heavy machines.