the disc is most likely a dvd, since most disc-based consoles use these now.
unfortunately, due to the tiny nature of the dvd laser (which, if you're interested, is 3 times smaller than a regular cd laser, in order to cram in the extra storage space), the slightest of scratches can throw the laser off course, causing loading problems, freezing during video clips, etc. some dvd players are more robust than others, but this is usually limited to dvd video players. i've yet to see a games console with the robustness to read any disc thrown at it, even if it has been thrown under a truck.
the thing is, there's only so much you can do to try and "buff out" the scratches. if you continually keep on trying, y ou may end up making the problem worse. and depending what cleaning fluid you're using, could start to melt away the plastic (that's right, i've seen that happen once or twice!).
if i were you though, i'd take it back to the store as faulty and get a new one. there's no way you should have been sold a scratched disc. if the package isn't shrink wrapped when you leave the store, get a new one. this way you can guarantee that when you get home, the disc will be in pristine condition.