Start with exit pupil: aperture divided by magnification. It is the width of the light beam that reaches your eye, and it should roughly match your dark-adapted pupil.
A 7×50 gives about 7.1 mm. That is bright and forgiving, with a wide field, but in a light-polluted sky some of that beam can be wasted on a pupil that never opens that far.
A 10×50 gives 5.0 mm — a good match for a dark-adapted eye. It will show Saturn as a small oval and resolve the Pleiades into stars, and most people can hand-hold it for useful stretches. For a first astronomy binocular, 10×50 is the balanced choice.
A 15×70 gives about 4.7 mm and gathers more light, but the extra magnification magnifies hand shake too. It wants a tripod or a very steady brace, which changes what kind of night you are having.
This guide compares types, not specific models, so it carries no purchase links. When you are ready for the short kit list, see the Starter Kit.