I'm sure you will get plenty of input.
I have an F-250 and am most familiar with Ford products so I'll take that bite of the pie.
An F-150 is a light truck, with an entirely light duty suspension and a GVWR of around 9,000lbs in it's heavies configuration. Perfect for hauling a pop-up trailer or something in the 1500lb range of truck campers.
An F-250 is a slightly lighter version of an F-350. It has the exact same axels and drive train as an F-350, unless ordered with "camper package" and/or a heavy duty suspension is has a slightly light spring pack with no overload springs or sway bars. It also could come with slightly lower weight rated tires and a max GVWR of 10,000lbs.
When you pay the extra $350 dollars and buy a truck with an F-350 badge you get overloads springs, heavier rated tires and a max GVWR of 11,500lbs. Other than that it is the EXACT same truck as an F-250. Ordering a heavy duty suspension on an F-350 might net you a slightly stronger rear axel or a beefier front end if it is a 2WD truck.
If you order a dually F-350 or F-450 you get a different truck, it has six tires and an even higher GVWR, a lower gear in the rear axel and is an even bigger, heavier duty truck.
Every Ford diesel pick-up has the exact same engine and trans combo. That being said, transporting children in the back of a pick-up truck is not the greatest idea. Maybe you should consider a full sized passenger van?