First things first. Your picture shows the bead separated from the rest of the tire. It's a good bet that was caused by a mis-adjusted brake rubbing against the tire. Fix the brake first, and you can prevent a repeat on an $80 Rene Herse or a $15 Kenda tire.

I like the Panaracer Pasela (fill in the blank) tires, but I think they top out at 38s. You probably won't notice the difference from 40s. Continental Top Tour or Top Contact are pretty decent; kind of heavy, but that also means less likely to puncture.