Craig, size for binoculars refers to two things - the magnification and the diameter of the field lens (or aperture). That's what the numbers mean - eg. 10x50 means magnification of 10 and aperture of 50mm. You want aperture to collect as much light as possible and magnification to see finer detail. Now any pair of binoculars will be better than the naked eye for seeing the sky. You probably want nothing less than about 7x40 and probably not more than 10x50. If I presume that you just wish to hold them up and look through, the upper limit is a matter of weight (those arms get tired) and being able to hold them steady (higher magnification needs steadier hands). Moving beyond 10x50, most people would find benefit in having some form of tripod or mount to resolve these two problems.
There are specialist optical/astro suppliers who can supply a competent pair for around $100. Be careful buying from other places that don't understand astro requirements. They may try to sell you a pair with ruby (red) coatings designed to cut down sun glare for bright daytime viewing, or less than fully multi-coated (FMC) surfaces, both of which can mean light loss from reflections - no good when you are looking for faint nebula and galaxies.
Search for various binocular threads on the forum - several give good articles to read so that you know what you are looking for in a pair.
Eric