For binos, get a pair under 10x, 10x is pretty much the upper limit. Anything above 10x is useless handheld, you need to mount them on a tripod otherwise the shaking will make you dizzy.
The lens size, depends on if you want a compact bino or something big. The bigger the size, the heavier the bino but also makes the image brighter.
The key thing to look at is the design, there are two designs, porro and roof. Roof binos have two parallel straight tubes, they’re more compact. Porros have a bend in the tubes, also known as a dog leg design. For cheap binos, anything under $150, stick with a porro design. Cheap porros will have much better quality optics compared to cheap roofs. Roofs require phase correction to be good, and phase correction is not cheap.

Nikon EDG Binoculars

Grace asked:

I don’t want to spend a lot of money, preferable $75 or less for a second pair to keep in my truck just in case I need them. I think I want 8x optical but the second number (i.e. 32, 42, 50, etc) what does it do for you? I want something clear and good for low light situations, so do I want a higher or lower second number? Also I was considering the Bushnell 10×42 Permafocus. . . does anyone have any other recommendations? Thanks

Reply:

When scanning for animals there are actually two considerations. One is power and the other is field of view. Unfortunately, the higher the power the smaller the field of view. A pair of 8×21 binos might have a field of view of 383 ft at 1000 yds. That is reasonably wide. 10×26 binos might have a field of view of 285 ft at 1000 yds. 1/3 less. With even higher magnification the field of view becomes even much less. Now there are 8 power binos that have even a wider field of view. Bushnell Legacy 8×42 WP have a field of view of 430 ft at 1000 yds.
Another important consideration is eye relief. That is the distance from the eye piece that the eye can be and still see the full field of view. Some binos have a very short eye relief.
In general 8 power binos are preferred by most users because they are relatively free from motion share which higher power binos are not.