First off, binoculars are designated magnification x diameter of objective lens in mm. Dividing the second by the first gives you the diameter in mm of the beam of light emerging from the eyepieces ("exit pupil"). That's important because the wider the better up to ca 7 mm, which is the widest your pupil can expand. However there is a tradeoff, because the wider the objective lens, the heavier the bins and the harder they are to hold steady. The optimum for normal lighting is an exit pupil of around 5 mm. For most people the optimal trade-off seems to be 7 x 35 or 8 x 42. Some can hold steady at 10 x 50, but those are hard on older hands and wrists. And the closest focus should be no more than 15 feet and better 10 feet for birding. 8x bins roughly correspond to a 400 mm lens in perspective. Good brands are Nikon, Leupold, Brunton. In general you can get quite decent glass for $150 to $200 and you can go on up from there to well above $2000. For a beginner with older hands and wrists look for a 7 x 35 to 8x 42 "roof prism".
Will