The answer, as is often the case for such questions, is "it depends". It depends upon things like (a) how large the integers are, (b) whether the input array contains integers in a random order or in a nearly-sorted order, (c) whether you need the sorting algorithm to be stable or not, as well as other factors, (d) whether the entire list of numbers fits in memory (in-memory sort vs external sort), and (e) the machine you run it on.
In practice, the sorting algorithm in your language's standard library will probably be pretty good (pretty close to optimal), if you need an in-memory sort. Therefore, in practice, just use whatever sort function is provided by the standard library, and measure running time. Only if you find that (i) sorting is a large fraction of the overall running time, and (ii) the running time is unacceptable, should you bother messing around with the sorting algorithm. If those two conditions do hold, then you can look at the specific aspects of your particular domain and experiment with other fast sorting algorithms.
But realistically, in practice, the sorting algorithm is rarely a major performance bottleneck.