Cookware Recommendations

So how big a difference does the cookware really make?

Can you really taste/tell the difference between a dish made in a skillet/pot that costs hundreds of dollars vs the same exact dish made with the same exact ingredients made in a $20 pan from Walmart?
absolutely, especially if you make gravies, rouxs, or cream sauces, like alfredo sauce.

Cheaper alloys do not distribute heat evenly, and the metal directly under the flame will get VERY hot, but the metal on the outside of the pot doesn't get as hot. Also some alloys will warp when heated with high heat.