First number is magnification, second is the diameter of the front lens. Greater the magnification and larger the object lens narrower the field of view in degrees and greater the problem with holding the glasses still.
If you hold a pair up and look at the eyepiece, you’ll see a dot of light, the bigger this is, the more light the glasses allow through, making them better for low light use. 10×50 = 50 ÷ 10 = 5mm diameter exit pupil, making them the optimum size for general use, but it does make them fairly heavy, 8×42 or 8×32 are probably the best all-round, 10×40 slightly lighter than 10×50, 10×32 less useful in dim light, 32 ÷ 10 = 3.2, etc.
The likes of the RSPB have days at wildlife reserves where you get the chance to try a large range of binoculars and telescopes, possibly worth checking out.
My pair are 8×32’s, which are small enough to stick in a large jacket pocket, are light enough to carry round my neck all day without getting uncomfortable and are probably the best size for all-round use.
But worth going to a good dealer and trying, rather than just buying a cheap pair from t’interwebz; quality can be really variable, and £150 is a good starting point.