Comparison Sort Summary

Sort	Time (avg)	Time (worst)	Space	Stable
Selection	$O(n^2)$	$O(n^2)$	$O(1)$	No
Insertion	$O(n^2)$	$O(n^2)$	$O(1)$	Yes
Merge	$O(n \log n)$	$O(n \log n)$	$O(n)$	Yes
Quick	$O(n \log n)$	$O(n^2)$	$O(\log n)$	No

Use insertion sort for small arrays or nearly-sorted data. Use merge sort when stability matters or you need guaranteed $O(n \log n)$ . Use quicksort for general purpose (with randomization).