Chroma-key green or blue are the most commonly used; the easiest will depend on the colours involved. For instance if you have fair-haired, light-skinned children in white or light-coloured clothing, than a dark background would make the selections easiest and vice-versa. Almost all selection tools rely in large part on relative contrast, and the greater the contrast and the more distinct the contrast boundaries are, the better the mask will be.
As Derrel mentioned above gray is the go to for background swap. The amount of masking required is minimal and fast when combined with the overlay blend mode, in Ps, even when you have lots of hair.