If you're going to be touring mostly on-road, you can ride just about anything, width-wise. 37/38 might be a little cushier since you can drop the pressure a bit, 35 or even 32 might be marginally (but almost certainly not significantly) faster. Off-road, wider tires have an advantage, since they have more area to distribute the load on sketchy surfaces like sand or mud.
Tires are a wear item, like brake pads. Unlike brake pads, it doesn't matter much which one you choose, as long as you avoid knobby tires. It's almost a fashion. Listen to all the yelling and listen to the person whose yelling you like the most. Next time, a couple thousand miles down the road, you can choose something else or start yelling yourself.
As for rims, Alex Adventurer look perfectly adequate for any of the above tire widths. If you go below 32 tires, you might want a narrower rim. Velocity Dyad and Mavic A317 are also good, and Sun CR-18 can be built into a good wheel. After you build the wheel, you can forget it until the rims are worn out (except for repacking the hubs every year or two).