With a very large number $N$ of points and a small subset $M$ to be chosen, it may be helpful to consider what is known about continuous versions of the problem in two-dimensions.
L. Fejes Tóth ("On the sum of distances determined by a pointset", Acta Math.
Acad. Sci. Hungar., 7:397–401, 1956) showed that the set of $M$ points on a circle which maximizes the sum of pairwise distances is achieved by vertices of a regular $M$-gon inscribed on the circle.
He subsequently (L. Fejes Tóth, "Über eine Punktverteilung auf der Kugel", Acta Math. Acad. Sci. Hungar., 10:13-19, 1959) posed the more difficult problem of maximizing the sum of pairwise distances for $M$ points in the plane whose diameter (maximum pairwise distance) is $1$. This problem remains open in general, although Friedrich Pillichshammer has given an upper bound and shown it to be sharp for $M=3,4,5$ ("On extremal point distributions in the Euclidean plane", Acta Mathematica Hungarica, 98(4):311-321, 2003).
These few cases suggest that the points of such extremal distributions will tend to occur on the periphery of a region. For $M=3$ the solution is an equilateral triangle with edge length $1$. For $M=4$ three of the points again form an equilateral triangle and the fourth point is located at the midpoint of a circular arc through two of the points, centered on the third point. For $M=5$ the solution is a regular pentagon of diameter $1$. None of these present a "scattering" of points through the interior of a figure.
If we wish to avoid predominating selection of points at the periphery, a different objective is apt to prove useful. The maximization of the minimum distance between points is such a criterion. Related problems have been broached at StackOverflow, at Computer Science SE, at Math.SE, and at MathOverflow.
For some insight into why this approach yields points interior to a figure, consider its rough equivalence to packing $M$ circles of diameter $D$ inside a figure. The $M$ centers are then points no two of which are closer than distance $D$. The picture in this Math.SE Answer will likely be worth a glance, showing how to best arrange ten points in a square.