Parking, never a problem, we work in mostly residential areas. It can be on the job for one day to a few months. When possible I will back it right up to the door or where ever the project is. People don't seem to mind if I back it across their yards. I very rarely take it to the lumber yard, have truck and dump trailer for that. Stocking, well, if I was specializing in one thing I would stock up on things like you said, but we do soooo much that it would be impossible to stock it. I do carry 25# boxes of drywall screws, torx screws, paslode nails, hand drives in two sizes etc, etc.
I carry misc. caulking, spray bin, misc step flashing, some pieces of *****, vycore etc. etc.
You know, you have me thinking now, I carry a TON of stuff, mostly tools but there are so many other things in there that I just take for granted.
In the front I do have a craftsman roll around 4 drawer tool chest mounted permanently full of hand tools, fuel cells, sand paper, safety glasses, ear plugs, vinyl siding tools, etc. etc.