To cope with Internet video explosion, recent work proposes to deploy caches to absorb part of the traffic related to popular videos. Nonetheless, caching literature has mainly focused on network-centric metrics, while the quality of users' video streaming experience should be the key performance index to optimize. Additionally, the general assumption is that each user request can be satisfied by a single object, which does not hold when multiple representations at different quality levels are available for the same video. Our contribution in this paper is to extend the classic object placement problem (which object to cache and where) by further considering the representation selection problem (i.e., which quality representation to cache), employing two methodologies to tackle this challenge. First, we employ a Mixed Integer Linear Programming (MILP) formulation to obtain the centralized optimal solution, as well as bounds to natural policies that are readily obtained as additional constraints of the MILP. Second, from the structure of the optimal solution, we learn guidelines that assist the design of distributed caching strategies: namely, we devise a simple yet effective distributed strategy that incrementally improves the quality of cached objects. Via simulation over large scale scenarios comprising up to hundred nodes and hundred million objects, we show our proposal to be effective in balancing user perceived utility vs bandwidth usage.