I've never heard of shedding before.
Polyester blend sheets will pill. As the fabric begins to wear, the threads poke out. These threads are too strong to break, so they form little balls. It doesn't matter how much they cost, all polyester blend sheets will do this.
Cotton sheets will become thinner. The threads are not as strong as polyester, so when they poke out (usually more often than polyester), they break off. All cotton sheets will do this.
Sateen sheets are softer, but have a shorter life due to the nature of the weave. High thread count sheets also are very soft, but have a shorter life because the threads are thinner.
Polyester blend sheets will last longer. They can still be used if pilled, although they will not be very comfortable. 100% cotton sheets will not last as long, because they will eventually loose so many threads that they will develop a hole. However, cotton sheets remain soft for their entire life, while polyester blend sheets do not.
Blended sheets are less expensive than all-cotton ones. The longest-lasting type of cotton for sheets is Pima, which is very expensive.
To make your sheets last as long as possible, wash in cold water on the gentle cycle. Then hang them to dry.