If you don't have above average ability to hold them steady, or you are going to be using them with a solid rest more often than not, you may find magnification above 7x or 8x is counterproductive because it magnifies the shaking of your hands.
Also, for any given quality of glass and coatings, a bigger exit pupil gives a brighter image. But the maximum pupil opening of the human eye is typically 7mm as a young adult, shrinking to typically 5mm by your forties. If the exit pupil of your optic is bigger than that, the extra light is wasted.
The exit pupil is discovered by dividing the objective lens size by the magnification, e.g. a 7x50mm bino would have a 7mm exit pupil and to get that exit pupil at 8x magnification you need a 56mm objective lens. So more magnification requires either a bigger objective lens (the bulk may become inconvenient) or reduces the exit pupil and it doesn't work as well in low light. For older users, a 7x35 or 8x40 will get the 5mm exit pupil that may be the most brightness they can use, in a more compact package.
The other factor is the field of view. More magnification at the same objective lens size will reduce the field of view. If you are scanning for game, giving up too much field of view will be a disadvantage. (A bigger objective lens may be desirable for this reason even if it is giving a bigger exit pupil than you need.)
At any given lens size and magnification, quality of glass and lens coatings can make a difference to brightness and clarity of image. Really good stuff can even overcome some of the advantage of the larger exit pupil in a lower quality binocular. But at the low budget end, to get the most for your money you need to keep it simple and don't go for the really high magnification. And look in the EE for sellers with a good reputation, you might get a better used bino than $250 will get new.
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