My favorite brand of baskets is the Val Pak brand. Available for a variety of skimmers and pumps, these baskets are more than 3x the thickness of a standard basket. Not only are they really tuff and hold up for years, the built in molded handles won't break, or pop out like the handles of cheap baskets.
Another great benefit of the Val Pak skimmer baskets like the one Im showing in this post, is the weight on the bottom. Cheap baskets have little, to no weight to hold them down, so they float up when ever the pump isn't running. It's not uncommon for people, or pool professionals to add small rocks to weigh the baskets down, or even twist tie fishing sinkers [small lead weights] to the bottom of a basket to keep it from floating up. When baskets float, it allows leaves and other debris to get under the basket, or the basket can get turned upside down, making the skimmer useless. Val Pak stays put whether the pump is running or not. It's an awesome product and well worth the money.