Tpreaves, Elizabeth and Lostbears all have good advice. As to whether you replace the CD cable or the amp cable first, I would think the amp cable, but the suggestion to try both is important because the outcome is going to depend on both your gear and the cables you choose. Some additional comments on the subject:
At the price of the Pangea cables, I don't know how you can go wrong.
The Shunyata Diamondback cable is very good, providing a large portion of the performance of the company's much more expensive and exotic cables at a fraction of the price, especially so at half price. It is probably well worth the $125 asking price and would also probably work very well on both your amp and CD player compared to your stock cables. I am using one right now on a Cambridge CD player and would never go back to the stock cable.
Spurred by the success with the Diamondback cable, I have also built my own cable, replacing a hardwired stock power cord on an older integrated amp using some Carol cable and a Pass and Seymoour plug. It cost $17 in materials from the local Home Depot, took about 45 minutes to make, and it sounds much better than the old stock cord.
If you were to build one of these for an application that requres an IEC connector as well as a male AC plug (most current applications), it would run you nearly forty bucks since IEC plugs for 12 guage and larger cables sizes cost at least $17 each. At this cost point, you are running into the cost of cheaper mail order cords like the Pangea, and you might as well save yourself the trouble and just buy one already made. Home made cords make sense to me when you are going to push the boundaries in terms of raw wire and connector quality, because the costs of these materials seem to get multiplied in the manufacturer's profit margins for premium hifi power cables.
Here are some other sources of budget cables you might check out:
http://signalcable.com/
http://zebracables.com/
http://www.audioadvisor.com/
http://www.thecableco.com/
Good Luck
