Which sorting method has best perfomance in terms of storage and time complexity?

Quicksort will usually be the best performing sort. However, quicksort has a worst-case time complexity of O(n2), which may not be reasonable in a real world application. Heapsort is often used in place of quicksort in these cases, as it has a worst-case of O(n log n).

The last of the "big three" sorts is mergesort, which Excels in a few areas. Mergesort is trivially easy to parallelize, which is increasingly useful as multi-CPU machines become more and more common. Mergesort is also a stable sort, which may or may not be useful for a given application.