The most important part of choosing the right binocular for birding is determining
your primary use for that binocular. No one model or brand is perfect for every habitat, climate, terrain, weather, or light condition - so don't try to find one binocular that does everything perfectly. That binocular does not exist. Instead, pick the binocular that's best suited to the type of birding you're most interested in. That way, you'll get the most pleasure from it in the long run, and the binocular will probably be more than adequate for any other observing you might do.
If much of your birding is done in forests or woodlands, for example, with mixed growth and both high and low overstory (where light is both refracted and reflected), a close-focusing 7 x 35 might be the instrument of choice. The popular 10 x 40 binoculars, with their narrower fields of view, are often too powerful in situations like these, where both light and distances are limited. Higher power binoculars often have a shallower depth of field, as well as not focusing as closely, which can make it difficult to locate a small bird in a haze of out-of-focus foliage. A low power, wide angle binocular like a 7 x 35 gives you a smaller bird in a bigger picture frame, but one with lots of sharply-focused habitat around him to reveal his behavior.
Consistently overcast sky conditions, however, or frequent use in shadowed woods and forests, may call for a larger aperture (such as a 7 x 42) to make the most of the limited light.
Close-in backyard and neighborhood birding and nature walks often need a compact binocular for more convenient carrying, plus a moderate magnification
for steadier hand-held use. Since most of these activities occur in the daytime,
the greater light gathering capacity of large aperture binoculars is usually wasted,
and smaller 20mm to 32mm objectives in a 7 to 8 power range are usually sufficient
- and more convenient to carry.
If you're fascinated by rookeries on distant cliffs, or
birding for skittish gulls and terns on miles of deserted beaches, a higher magnification 10 power binocular may be just the ticket. Since lighting is less of a problem under such conditions, an aperture in the 35mm to 42mm range is usually all you need, and a waterproof or showerproof model might be appropriate. Even 40mm binoculars can be sometimes excessively bright for seashore and pelagic birding, due to highly reflective sand and multiple reflections from sunlight on water. You can reduce eyestrain and headaches due to such excessive brightness by moving to a smaller
aperture binocular.
A large aperture binocular of 8 to 10 power and up is useful for early morning medium distance fixed position birding at lakes or marshes. It is also good for nature studies of whales, sea otters, mountain goats, etc. Its use usually requires tripod mounting for steadiness.
An 8 x 56 binocular is often the instrument of choice for raptor watching, as its great light gathering allows identification of underwing patterns when high power but smaller aperture binoculars see only a black silhouette against the bright sky.
Many birders consider a 10 x 40 binocular to be the ideal size. However, you should consider the drawbacks mentioned above (usually a narrow field of view and a shallow depth of field) if considerable close-in birding figures prominently in your plans. It may be that two different binoculars will suit your needs best - a 10 x 40 or 10 x 42 for long distance birding, plus a wide angle 7 x 35 or 8 x 32 for close-in work.
If your budget limits you to just one binocular, however, one of the 8 power models in the 30mm to 42mm aperture range might be the best compromise. Typically available in a variety of sizes, weights, and prices, they offer good twilight factors and usually quite reasonable close-in performance, while still having enough power for long distance work - all in a size small enough to be easily portable and hand-holdable. The old expression "jack of all trades, and master of none" probably best characterizes the performance of binoculars in this power and aperture range.
No matter what power and aperture range seems best to you, however, keep in mind some other important considerations - eye relief, binocular weight, and your budget.
If you wear glasses when observing, look for long eye relief so you can see the full field of view.
If you carry your binocular whenever you go walking, or spend long periods with your binocular raised to your eyes scanning woods and sand dunes, look for reasonably light weight. But don't pick a binocular strictly by weight. A binocular weighs only a fraction of what your arms weigh. What tires you out when using a binocular is not the weight of the binocular, but the weight of your arms.
There's a case to be made for choosing a binocular with a little extra heft to it - as the extra weight soaks up minor hand tremors and makes for steadier viewing. A few extra ounces won't tire you out that much faster, but it might let you see more clearly. Just be sure you have a wide neckstrap for those heavier binoculars to make carrying them easier.
As far as your budget goes, keep in mind that doubling the price you pay for a binocular does not mean you get twice the performance. Some of the higher cost goes for features instead of optics - leather cases instead of vinyl, more comfortable wide woven straps instead of narrow plastic, rainguards, etc.
As a general rule, each doubling of the retail price of binoculars from $50 or so up to $200-$250 results in a 20% improvement in optical
quality. However, beyond $250 each doubling of the price results in only a 10% improvement. A $1000 pair of binoculars will not be four times as good as a $250 pair, even though they cost four times as much, but a $250 pair will be visibly much superior
to a $50 pair.
Get the best optics you can afford. Good optics will last a lifetime. So-so optics will have to be replaced frequently - and several inexpensive binoculars will end up costing you more in the long run than one good-quality binocular.
Over a ten-year lifespan (although it will probably last much longer), a $200 binocular will cost you only 19¢ a week more than a $100 binocular that you may have to replace after a mere two or three years. But that $200 binocular will give you much more than 19¢ worth of extra clarity, sharpness, and sheer enjoyment every time you look through it.
Good optics are not an expense. They're a lifetime investment - and investing in quality always pays dividends.