If you plan to keep this bike and your safety is worth the investment, I would get new brake calipers, and pads. Tektro dual pivot calipers are reasonably priced, and made for the newer style replaceable pads. I have a Schwinn World tourer with steel rims that I installed Tektro's on, and Kool Stop salmon pads. The salmon pads are listed as wet weather pads, but are fine for wet or dry riding. A side benefit of the salmon's is less 'brake pad debris' on your rims. I use them on alloy rims too, for the stopping power, and cleanliness.
You MAY be able to find pads to fit your sidepulls, but if safety is your main concern, I would highly recommend getting the Tektro's. I also agree that cables/casings should be replaced. New calipers will make a substantial improvement in your braking power. Salmon Koolstops will make THAT better. These are MY opinions, and YMMV.