I agree with much of the above with a few exceptions. I believe a wheel built with double butted spokes is lighter and stronger than one built with straight gauge spokes. I do not believe that you need a deep V rim. They are heavy and will look grossly out of place on something like a Schwinn Traveler. I also do not believe you need a rear wheel with 40 spokes (which greatly reduces your choice of hub and rim).

A modern 126mm rear hub with sealed bearings, laced 3x to a good quality rim with 2.0 or 2.0/1.8/2.0 spokes with a 32-35mm tire will cure your ills. A Velocity Dyad would be a great choice, but a Sun CR-18 will work perfectly well for you and look classic doing it.

I built my dad, who is exactly your height and weight (maybe a few pounds more) a wheelset with VO hub (Sanyo front), 700c CR-18s, Sapim Race spokes and 35mm Soma tires and he's not had a problem, though he doesn't put in a lot of miles.

A bicycle is three main parts; a frameset, a wheelset and a component group. A good, handbuilt wheelset is an investment, yes, but one that can be transferred to another frame in the future.