Properly adjusting and lubing your brakes is the key to keeping good brakes. You want your brakes to have a snap to them and to feel them make contact with the rim. Squishy brakes are generally a bad thing.
You want to make sure that both pads are laying flat against the rim. To properly do this not only must the position of the pads be adjusted but the wheel must also be trued. Also, it helps if the rim has a machined or anodized sidewall (as opposed to a painted one). You've already go this covered. Wipe the rims with degreaser. As far as brake composition, nice rubber pads work fine to my experience and always be careful not to contaminate the pads with degreaser or lube.
Make sure the pads are an even distance from the rim. If you have newer caliper brakes, there is probably a set screw on the side that allows you to adjust the brakes from side to side and maybe one for the distance between the brakes. The old caliper brakes require you to change the alignment by adjusting the bolt attaching them to the frame. If your brakes squeal, it can help to have this alignment a hair off.
Make sure the cable housing is lubed properly and that the cable is not fraying anywhere (this is also a safety thing). The cable likes to fray down at the pinch bolt on the brakes that holds it in place. When I've installed a new cable, I like give a nice hard pull on the brakes. This helps to ensure that the cable is stretched. Some cables claim to be prestretched, but I do this anyway just in case.
Also, it helps to lube any pivot points in the brake itself. I don't go wild here, just a few drops of lube in each pivot point. Make sure the all bolts and screws are sufficiently tighted. That's all I can think of right now.
EDIT: To answer some more questions, dual pivot is generally more effective. However, like everything else it depends on the quality of the brakes and how well the brakes are adjusted. Cheap single-pivot brakes scare me, though. Brakes flex when you hit them, and cheap single-pivots flex a lot when you hit your brakes hard.