If you get binoculars that are more powerful than 7X or 8X, you won't be able to use them because the image bounces around too much. The reason most binoculars are 7X (7 times magnification, or 7 power) is because at this magnification, the image is stable and the field of view is wide.
You want a wide field of view because it is more like your own eyes -- it feels natural. A narrow field of view is like looking through a keyhole. You won't like it, and you won't use the binoculars. The higher the power, generally speaking the narrower field of view.
The 50 number refers to the size of the lenses at the front of the binoculars -- 50 millimeters. This is a good size. The larger the big lenses (called "objective lenses") are, the brighter the image, and the sharper the image. For lighter binoculars, go with a 35 mm. objective lens on your binoculars.
About the best balance of power and useability is 7X50. This will give you a bright image, a wide field of view, a stable image that doesn't dance around, and will be light enough to carry easily. It's all about balance with binoculars. You have to balance positive features with negative features.
I would strongly advise against getting ten power (10X) binoculars. That's a little too much power to hold in your hands. You will need a tripod for a stable image, and nobody wants to have to use a tripod with a set of binoculars.
I derped. Started to reply this to OP (in less detail), got stuck on the phone with a client, finished and there you were. Well said. 7x50 is optimal.
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