PU leather, aka Bycast Leather, is Reconstituted Leather (small leather scraps) or Bonded Leather that is layered with thick Polyurethane to give it a sheen like real leather. The image of such a process that comes to my mind is like gluing scraps of wood together and pack it really tight to look & feel like real wood.
Since it is synthetic material, it doesn't last as long as real leather. However, for a handbag, I personally think it is ok to use. For shoes, I wouldn't recommend it though, as shoes tend to wear out faster and Polyurethane is not a breathable material like leather.
As for sheep skin....well, within the accessories industry (bags, belts, shoes, planners, etc), they classify any animal skin (cow, calf, lamb, sheep, even pig) as "leather."
For handbags, it really depends on what type of look & feel you want and how much you can afford to spend. Just because certain designer brands label certain products as Sheep Skin does not necessarily warrant charging consumers an arm-and-leg price. After you read that link, go to different stores, from Wilson's Leather to expensive designer brands, close your eyes and feel with your hand the various textures of each grade you come across. Don't let the trendy colors and glossy coating fool you into paying too high of a price, as they do often use glaze to give lower-grade leather a smooth, lotion-y type of false softness.
