Main reason to go with E-350 or 250 vs a 150 is higher GVWR, bigger brakes, full-floating axle, etc. It matters a lot for weight carrying but even more for offroad use. Traveling down the highway loaded upto GVWR would probably be fine but trying to move around off-road in the dessert or up a mountain at max capacity won't work so well. Axles, springs, driveshafts, etc break under those conditions.
A big van is easy to fill up with stuff and stuff = weight.
My E-150 GVWR = 6,200lbs and it weighs 5,000lbs so I can add 1,200lbs of stuff. A E-350 gvwr might be 9,500 and it might weigh only 750 more than my van, so it could haul maybe 3,750lbs of stuff. That's a big difference in capacity and it's usually a small difference when it comes time to purchase a van for E-150 $ vs E-350 $. Not to mention WAY more E-250 and 350 are available on the used market.
For gas engine choices, I really like the 4.9L 6-cylinder, manufactured by Ford from 1966-1996. They were installed by Ford in everything from F-100 pickups to F-600 dumptrucks and used by the military in a variety of equipment not to mention being the preferred engine for UPS box trucks for decades. They're not powerhouses but are torquey, extremely reliable, easy to work on, and cheap to maintain. If you want more power, I'd go V-10 or 5.8. The EFI 460(7.5) isn't powerful enough without modification to offset its poor mileage and the 302 (5.0) isn't up to the task IMO.
You said you have a handle on the diesels so I'm not going into that much but be advised there are 2 VERY different 7.3L engines, plus the 6.0 and a 6.9.