I'm with Tallpine, regarding trailer & tow vehicle: a 5th wheel or goose neck is so much easier to tow & maneuver. Full-sized van + 25' standard trailer + no help will keep you out of a lot of trailer grounds in places you'd really like to go.
My dad & step mom did this for ~1 year with a 25' 5th wheel light enough to be hauled by a 1995 Dodge Ram 1/2 ton with 318 V8, 4spd auto, & 3.73 rear end. It was short & maneuverable enough (ext cab & short box) that they did not encounter any grounds that they could not squeeze into. In retrospect, my dad would have preferred more vehicle, minimum a 360 V8 or a 3/4 ton PU with any appropriate engine (360+ gas or diesel).
The E350 diesel is enough tow vehicle, but as TP writes, vans are a SOB to work on.
My ideal tow vehicle would be a 3/4 ton or 1 ton (non-dually) 4-door PU, diesel engine, manual tranny, goose neck trailer. Truck bed would have a quality big ol' truck box up front. I'd have one of those soft camper shells to use if I was tooling around w/o the trailer and wanted covered area. I could sleep in the back seat, or the bed on my electric-pump-inflatable mattress under the soft shell.
The trailer wold be a goose neck metal frame, or at least one of the better quality others. If only me & maybe one other, and our mission is to go neat places, 25' would be ideal. If more a "mobile house," that moved around the country from work site to work site, I'd want 35'-40'.
I'd definitely spring for the side awning and would also have a screened, covered area to serve as a foyer, outdoor eating/whatever area to serve as a "mobile mud room."
A utility bicycle on a mountain bike frame would be an invaluable accessory.