From many years of commuting, I determined that anything under 1.75" in width made the bike too squirrelly to handle. I felt downright unsafe with 1.25" tires. I am currently rolling on these:
https://www.amazon.com/gp/product/B000OERSNY/ having had great luck with the discontinued Vittoria Adventure series. So far so good, although I have only a couple hundred miles on them. I run them at 70 psi, which is the maximum rated pressure. They stick very well in the corners, and the bike handles very well for a 1997 vintage 26" model. Here is a recent picture:
I have heard nothing but good things about Schwalbe tires, but I have no personal experience with them. I use Contis exclusively on my road bikes, but the Conti street tires I had on this bike flatted constantly from small bits of glass. I had similar issues with the equally expensive Michelins I tried. No such problems with the Vittorias. I see some negativity around the net because of rolling resistance, but when you use your bike to get to work, flat resistance is everything. I'm retired now, but I still ride this bike a lot. I never worry about it.