You might want to double-check the size of your rim and tires and make sure they're compatible. In your OP, you mention 700x1-1/4 tires, but also say that it's an older bike (the Schwinn Le Tour was made from 1972 to 1988). Note that older bikes used 27" tires which are NOT interchangeable with 700c tires. There's an 8mm (1/4 inch) difference between a 27" wheel (630mm rim diameter) and a 700c wheel (622mm rim diameter). If you put a 700c tire on a 27" wheel, the tire bead won't seat correctly and you'll get blowouts especially at higher pressure.

The Strata K tires that you linked to come in two diameter sizes. 27x1-1/4 and 700x28mm or 25mm (1" or 7/8"). Before buying tires, double-check the diameter of the rim. I'd be very surprised if a true 1-1/4" tire has a max pressure rating of 90psi. Most tires that wide have max pressures of 70-80psi, while narrower 28mm tires may go to 100psi or more. For rough roads, I'd stick with 35mm (1-1/4") tires.

To know the rim size, you may have to measure it yourself. The tire size is printed on the tire itself. Usually something like 35-622 which means the tire is 35mm wide and goes on a 622mm diameter rim. Real 27" tires are very hard to find these days, so the Strata tires that you linked to are a good find.

In general, I like to inflate tires to about 5psi below max on the rear and 10-15psi below max on the front. I put less pressure in the front because the front wheel bears less weight, and less pressure gives a softer ride with slightly better traction with your steering tire (where you really want better traction). More pressure in the rear will help minimize tire resistance so you won't feel like your wide tires are slowing you down.