There are a lot of variables. I have used 8x before while elk hunting and they were great. I normally use a 10x42 and a spotter but it just depends on what other glass you have if any. If you do not have a spotter id get at least a 10x42. I do not have rangefinder binoculars but if weight is a concern for you then thats something to consider. I do think that if you plan to run a range finder and bino they will most likely add up to be heaveier than a rangefinder bino.
I prefer binos and a separate range finder. But I think a 10x42 will pretty much get the job done everywhere you hunt. I have the Maven C.1 and I love them.
As was said above, it depends on the hunting conditions.
Don’t use cheap optics. You don’t need a top of the line pair of Swarovski’s or Zeiss, but get a decent pair of mid tier glasses that will serve you well for many years. With the newer technology, many brands perform really well.
I like 8x42 binoculars. The 42mm objective lens does well in low light. Has good dimensions and not too heavy. Larger than 42mm they become bulky and heavier than needed. 30mm lenses sometimes don’t do as well as needed in low light conditions.
I find magnification greater than 8x is not needed in most instances. When your tired, or breathing heavy from walking up a ridge, it is harder to hold higher magnifications steady. Or if you hands are tired from glassing all day. The field of view is also much narrower with 10x. When you have a narrow field of view, it can be more difficult to pick up animals moving through the brush. Or just finding them bedded on a hillside, since they may not be in your narrower field of view. In general, their is a noticeable difference in the field of view between 8x and 10x, with 10x being narrower. As far as magnification, sometimes 10x is more helpful than 8x. To be perfectly honest, an extra 2x magnification over the 8x isn’t going to make much of a difference in most instances. If your binoculars are set up on a tripod all day, glassing longer distances in open country, then a 10x may be best. For me, the advantages of an 8x outweigh the advantages of a 10x in most situations.
Don’t get a pair of binoculars designed more specifically for bird watchers. They may be built lightly and not designed for harsher conditions we sometimes face in hunting.
If you are buying new, I would look at Nikon Monarch 7 or Bushnell Forge both in 8x42. Both have real good glass, dependable and reliable. And of course their are many other well made binoculars from reputable companies. Best if you can try different binoculars, comparing them side by side. See what is most comfortable in your hands, fits your face well. If you wear glasses, make sure you can use them with your glasses on, without losing some of your field of view while looking through them.