Sweet. RG-6 isn't necessary but I would really recommend it. Most houses built in the late 80's to present were wired with RG-6. It's a thicker grade cable that holds signal strength better than RG-59. I forget the exact equations but for example for every 100ft of RG-59, you may lose like 6db. With RG-6 at 100 ft, you may only lose 3db. Less loss equals less noise in the lines, which means better picture quality on your TV's, and less packet loss through your modem.

Again it's not necessary to change it out, but I know my company is required to change it out if they see it on a "drop". A drop is basically the line that runs from your pole or cable box to the side of your house. In your case, the ground wire was inside the basement and normally that means the cable is going straight from your pole or cable box, directly into the basement. Newer homes have an ground block box on the side of the house closest to power.