First, RTFM, if I may boldly suggest. It will tell you 99% of what you need to know about everything on the vehicle. Even how to change the common light bulbs and perform other maintenance yourself.
Break-in is one of those topics where you will find many, many opinions. So many that you could spend several days on the net reading about it and only scratch the surface.
For me, as a Ford tech, I will suggest that for the first 500 miles you avoid long idle times, heavy trailer towing, long periods of wide-open throttle, and long periods of steady driving speed.
That last bit conflicts with your shopping trip, unless you plan on taking the back roads. It is important to vary the engine speed so that all moving parts operate together over a wide dynamic range, as different parts see different types of loads as the engine speed and power changes.
Also, I like to keep fresh oil in the engine as it breaks in, changing at 500-1,000-3,000-5,000 mile marks. But as I said, I'm a tech and can do this for very little money. You may not think it necessary nor economical to do this.
I will be buying a Brand New E350 van from out of state and will be driving about 800 miles (all Interstate Highway driving) to my home. I'll be going through the mountains the last 400 miles. How do you recommend driving it during this drive?
If I were doing the same thing, I'd try to vary the speed a little bit while on the flatlands. Take it up to your limit, then back off the gas pedal a good bunch and let it slow down to 15-20 mph lower, then accelerate back to your cruise speed, by any means you choose, either gently or with a bit of aggression. Backing off the pedal will raise intake vacuum, and pull a bit of oil or at least take the load off for a bit.
I pretty much did that with the vulcan in my old Sable that has gone 250k so far. Drove from Inpls to SF Bay area over two or three days, varying the speed pretty much the whole way.
You will have to face longer 'heavy load' times when climbing, but then can let off the gas completely on the way back down.
I did not bother with changing the oil until the car had thousands of miles on it. I figure the filter is there to do its job, and if the leftover machining 'chunks' were that big, they'd cause problems anyway. Everyone else will have their own opinion.
If the engine had just been re-ringed, I'd follow old advice of getting into top gear at around 45, and pressing as hard as possible on the gas pedal without an automatic downshifting, take it back up to 65 or so. Then coast back down again. Rinse and repeat about 10 times. Good load wide open will put pressure on the rings to get them to seat, without hi rpms. Vacuum on the coastdown will allow cooling and provide a bit of extra lube to the cylinder walls for those rings that are breaking in.
...I will suggest that for the first 500 miles you avoid long idle times, heavy trailer towing, long periods of wide-open throttle, and long periods of steady driving speed...
This is what I tend to do. I have only had 3 new cars, one I sold with 115k, another lasted 200k (until the cooling fan died and the wife didn't pay attention to the temp gauge) and the third is currently at 227k (2004 Tribute). All of them have been great and never burned oil.