I highly recommended Continental tires that fit right on and have EXCELLENT traction. I have a pair of Duros that would NOT seat properly no matter what.
Sometimes, it's the rim that determines how well a tire seats, or doesn't. I had a '79 Fuji S-12S that I could never get a tire of any brand to seat on. Once the pressure hit 70lbs, the tire would creep off the rim. Even my LBS gave up. The bike itself had not been ridden much and the rims had no damage.
The '73 World Voyageur I had was a different story. It took Park metal tire levers to get the bead seated. They were straight side rims and could be pumped up to 90lbs with no bead creep. This was with Kenda 27 1 1/4 gum walls. Very tight tolerances on these rims, which I believe were Arayas.
With the Chicago Schwinns, I have found it easier to seat tires on the steel S-6 rims vs the Weinmann alloy rims found on Super Sports, Sports Tourers, etc. My '71 Suburban and '74 Varsity are both equipped with Kenda 27 x 1 1/14