Tire size really isn't an issue with lots of weight. I've ridden 19mm (like little razor blades
) and I haven't strayed from 220 in 20 years. The tires held up just fine and, as long as you keep them inflated to the proper pressure, they never pinch flatted on me. They weren't comfortable but they were fast
If you want comfort, go with something wider than a 28. The ride is nice and smooth but, again, you need to keep them inflated to the proper pressure (much, much lower than the 19mm).
As for a bike to carry all that stuff, go with a real live touring bike. Not one that pretends to be a touring bike but something along the lines of a Cannondale T800 (my favorite beast of burden). The bike is a great big guy bike and is built to carry massive amounts of stuff for day, weeks, months and even years. And it not much of a schlub when it comes to speed either.