Hello PaulE. Are your rims steel and no hook? That will be a problem for modern tires. I put new wheels on my 1973 CCM that were 590 x 30, including a SA X-RD3. I have Marathon Plus on most of my bikes. Their only choice 40/ 584 size is actually 37 mm on my Dyad rims, perfect for my likes.
Get Schwalbe tubes also. I use schraeder valves that are 40 mm threaded. They hold air far longer. 60 to 66 lbs is what I run and I do 100 mile highway rides. I got tired of skinny 1 1/4" tubes and stuffed in the 1.75" tubes, that are 3/8" wider inflated. This bike has 8,550 miles since I got it in 2017, I just put one new tire on.
On a 2 day 150 mile ride. >>