7x50's are pretty traditional, since they give you a good compromise of weight, size, magnification and low-light capability. The two numbers, in case you don't know are the magnification (7x what the normal eye sees) and the size of the objective lens (50 mm or roughly 2" in diameter).
Higher magnifications than 7x will generally be harder to handhold steadily on a small craft, which is where the stabiliized binoculars come in to play. However, stabilized binoculars require electricity to work... and if the batteries fail, the much higher (10-14x) magnifications on most image stabilized binoculars will be useless.
The Objective diameter divided by the magnification gives you the exit pupil diameter. On a pair of 7x50's it is about 7.1 mm. This is important for estimating the binoculars low light capabilities. Anything less than a 7mm exit pupil will generally be significantly dimmer than unaided vision, and may make it very difficult to read the markers through the binoculars. They do make "night-vision" equipment that can help with this, but again, the NVG gear is close to useless if the batteries die.
A few other things to consider:
: Center or individual. Most waterproof binoculars have individual focussing, since it is easier to design a waterproof binocular that tway.
This is especially important if you wear prescription glasses. The better ones have almost an inch of eye-relief....which means your eyes can be an inch away from the eyepiece and still see the whole image properly.
You can have an analog or digital compass built into the binoculars. This makes taking a bearing very simple. The digital ones are often easier to read, at least until the batteries die.
I prefer the analog compasses.
Yes, they should be both waterproof and nitrogen filled. Non-nitrogen filled binoculars will generally have issues with condensation internally in colder weather.
You should either get a floating strap, usually with foam or neoprene padding, or get a set that floats. You will eventually drop them in the water, and it is best if they don't sink.
The better marine binoculars have rubber armor to help protect the binocular's optics from shock in the case that you drop them. You will drop them... so do your boat's gelcoat, your binoculars and your toes a favor and get them with the rubber armor. This also makes them easier to grip in bad weather and makes them warmer to hold in cold weather.
Finally, a good pair of compact binoculars, for general daytime use is a set of 8x30 binoculars, like the Steiner's shown here:
They're about two-thirds the size of the 7x50s I use at night, and give you a tiny bit more magnification. These live in my daybag.