First, we are talking about 26 x 1 3/8 tires here, right? Nothing oddball?

There is an abundance of choice in the 26 x 1 3/8 (ISO37x590) size, but if you must have "gum"walls for aestetics, that does limit things. Kenda, Pyramid and Chengshin all offer generic gumwalls in this size. Moving up you'll come to the Michelin World Tour and finally reach the previously mentioned Panaracer Col de la Vie.

Other worthy abeit blackwall tires in this size include the Bell Sports Streetster folding, Continental City Ride, Schwalbe Marathon, Specialized TriSport and Vredestein Perfect Tour. Kenda offers knobbies - which, now that I think about it, have tan sidewalls.

The three speed hub: we are talking about a Sturmey-Archer AW here, right? Nothing oddball?

Most likely it only needs to have its 40 year-old oil residue soaked out and then be relubricated. Should anything actually be worn out or broken (unlikely), all internal parts are still available from Sturmey for their 1936-1999 AW three-speeds. If you go with a new hub or wheel, Sturmey's current production S-RF3 hub (which uses the improved AW-NIG internal mechanism) will slot right in and hook up to the existing shifter and cable.

If the bike is going to be a rider instead of a wall hanger, the one modern upgrade I'd recomend is aluminum (a.k.a. alloy) rims. The Sun CR18 is offered in 26 x 1 3/8 with 32, 36 or 40 spoke holes.

tcs

P.S. No make that two upgrades. Get new brake blocks.