Best case for sorting algorithm
We usually measure the running time of algorithm as a function of the length of the input.

For example, when we say that an algorithm runs in time $O(n\log n)$, what we mean is:


For every input of length $n$, the algorithm runs in time $O(n\log n)$.


This is an example of worst-case complexity. In your case, you are looking for a function $T(n)$ which satisfies the following:


For every input of length $n$, the algorithm runs in time at least $T(n)$.
Furthermore, for each $n$ there exists an input of length $n$ on which the algorithm runs in time $T(n)$.


To answer your particular questions: the answer should be a function of $n$; and we are looking for the "best-case scenario" of the algorithm for each input length $n$. Whether this best-case scenario is the one you said or not, depends on the algorithm. There might be algorithms for which your best-case scenario is actually a worst-case input (we can construct such algorithms artificially).