Braking will be mediocre-to-poor as long as you keep the steel rims. Better brake pads will help a little, but even with the best pads, going downhill in the rain on a bike with steel rims is scary.

Is there something specifically wrong with the brake calipers on it now? The pictures don't show any imminent failures, unless I am missing something.

Also, if you were to replace your 26X1-3/8 rims with some 700C rims (change rim diameter from 590mm to 622mm, change in radius of 16mm), which might be possible based on the amount of clearance shown in the photos) you would get aluminum rims (better braking and stronger than steel) and you could use the existing brakes with the pads much higher, which would also give much improved leverage. Plus you would have a much wider choice of tires.

You could also just get a new set of aluminum rims in the 26X1-3/8 size... at least on the front where most of your braking takes place.