I don't know if testing for copper would really be necessary. If you want to, though, there are copper test kits you can buy on the internet.
As for the water, there are several options. You can buy a reverse-osmosis unit that you can run at your house, or do what some people do and buy gallon jugs of distilled or r/o water from Walmart or your grocery store. At the very least, you can buy the American Pharmaceuticals Tap Water Filter....I've used that for a while, and it seems to work really well, although the cartridges have to be replaced every so often, and in the long run, an r/o unit would be cheaper.
As for the skimmer, I've heard nothing but great reviews for the Coralife Super Skimmer. I plan to get one myself for my 55 gallon tank soon.