A 'good' pair of binoculars for astronomy is one with large objective (front) lenses and relatively low magnification. A standard to follow is

7x50 for truly dark skies (a sky where you can see the Milky Way clearly!) and good, widefield views of the Milky Way and open clusters.
10x50 is a good standard magnification and slightly more useful in low level light pollution. Good views of clusters and galaxies dependent on location.
20x50 will give a good view of the moon, but will need to be mounted on a tripod to keep them still.
Any pair of binoculars with an objective lense bigger than 50mm or a magnification over 15x will need a tripod. Large binoculars can be as expensive as small telescopes, but give excellent views of the Milky Way and star clusters.

There are a number of factors to consider when choosing a telescope. Many introductory books on the subject go into great depth about this subject. Generally you want a telescope with a large objective lense or mirror, the bigger the better. You should also look for one with a good, sturdy tripod- this is as important as the telescope itself! Flimsy tripods will lead to a shaky image and will render your telescope useless.

There are two main types of telescope- reflector and refractor. Refactors tend to be more expensive and use lenses to focus light. Reflectors use mirrors to focus the light. The minimum size of refractor would be around 3 1/2 inches or 80mm, the minimum size of reflector is around 6 inches (120mm). Having said that, there are many 4 1/2 inch reflectors with good tripods available.

Patrick Moore's guide to buying a telescope gives a more in-depth guide to buying telescopes and binoculars. Read it first before making a purchase.