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G'Day Rob,
7x50's are the classic astro binoculars. They have a 7mm exit pupil which is ideal for a fully dark adapted young eye. Unfortunately, as you get older your eye dilates less and eventually won't fit a 7mm diameter beam of light through.
8x50s and 10x50s will collect the same amount of light, and have a smaller exit pupil diameter, but the trade off for more magnification is less field of view and they get harder to hold steady. Above 10x I'd recommend you mount them on a tripod or rest of some sort.
50mm objective binoculars will theoretically gather 51x more light than the naked eye (assuming a 7mm pupil in your eye). A 40mm objective will capture 32x as much light, so you'll see 4 magnitudes dimmer than naked eye. 50mm will allow you to see 4.8 magnitude deeper.
You can certainly see the moon of Jupiter, and you'll see nebulae and galaxies though they will in most cases be little fuzzy patches. You will get the best views of the Pleaides with binoculars, and similar large objects in the sky that are too big for most scopes.
Al.
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