Some help on replacing brakes?

http://imgur.com/a/gCUjA

As you can see in the above album, I have a vintage early 1990's mountain bike I've re-purposed as a commuter bike to ride to the train station. Back when I used to take it on the trails the brakes took a few hits and now I can't get the pads seated properly, they hum, and I guess it's time for a new set but I'm clueless as to what I need.

I found these on Amazon and I was planning to get a front and back set, plus the little cable (what is that even called?) so the installation can go as fast and easily as possible. I'm interested to get a decent set without spending more than I need, and have also considered these.

I'm pretty handy with tools, but what's everything I need so I can do this easily in one fell swoop? Will the old bolts and pads fit? Should I even consider doing this to a bike so old?