The best deer hunting binoculars are those which are light and can easily be used by the hunter by hanging them around the neck. The ideal weight should be less than 25 ounces.
You can use some of the top brands which are there and these are here which you can check here in my last post about top binocular brands.
Some of the features that you need to look for while going for deer hunting are
What is the eye relief of the binoculars?
Weight as I said earlier is also a consideration
The best specifications will be 7×35 or 8×42
Waterproof and fogproof
Binoculars with a range finder is needed is you want to use the gun effectively but again cost will be much more.
Some of the latest hunting binoculars are the
EDG binoculars from Nikon
Zeiss’s victory RF binoculars
Bushnell’s PowerView 8-16x40mm
Peregrine XP binoculars from Steiner
Endurance DF binoculars from Hawke Optics
Apart from these there is really nothing which is needed as far as special binoculars which are there for deer hunting.
Any lightweight within your budget binoculars with the specification of 7×25 or 8×42 are good enough for deer hunting. If you want more flexibility and better views then you can use the hunting spotting scopes.