What is better to buy.....Aluminum Cookware Set or Hard-Anodized Cookware Set?

Neither. For one, stainless steel is the way to go. Secondly, with both of those you're paying more for the celebrity endorsement than you are the quality of the product. Go with All-Clad. If it's too expensive, you're better off deciding on a few pieces that you'll use the most and buying quality rather than an entire set.