"No Pain, No Gain" - Pain, especially that lingering sensation that you feel for days, is not necessarily the sign of a great workout. It is actually a sign that your body is adapting to new stimulus. If you continue with a similar exercise program at similar intensity, the soreness shouldn't return. You can minimize the soreness by starting light and gradually working into new routines. To read more about this subject, click here for an article from the American Council on Exercise.
"The Fat Burning Zone" - The idea here is that you burn a higher percentage of calories from stored fat in the fat burning zone compared to the cardio zone. True, but you burn more total calories in the cardio zone - think of it as getting a smaller piece of a much bigger pie. You actually get about 100% of your calories from stored fat when you are sleeping, but the total calories burned is very low. Focus on total calories, once you've established an aerobic base, and train in the cardio zone for best results reducing weight and burning fat. To read more about this subject, click here for an article from the American Council on Exercise.