Beginners will want to start with a magnification between 7 and 10 since these can be held by hand without too much jitter. Diameters of 50-80 mm can also be hand held. Cheap binoculars are only suitable for day use, as they lack corrected optics which prevent distortions away from the center of field. They also tend to have small exit pupils resulting in light loss. You should probably stick to astronomy vendors when buying a pair of binoculars, and pay attention to the eye relief if you wear glasses for astigmatism.
Telescopes also use a two number system, but they represent different metrics.
The first number is usually the diameter of the main mirror or lens, and is typically in inches until the diameter is below 3 inches, when it switches to millimeters. For a given eyepiece, a longer f-ration will result in a smaller field of view but a higher magnification. Beginners typically want to stay below f8. Beginners should put more emphasis on light grasp and less on magnification. A small diameter telescope with a high f-ratio is no fun for a beginner.