For someone just beginning in astronomy, I'd recommend handheld sizes, as their field of view is larger, making it easier to orient yourself to the sky and find things you're looking for. Even if you get larger binoculars later (as well as a telescope), you'll still use the handheld ones. A tripod and mount will improve the view with any size, but in general most people can handhold up to 10x50 fairly well.
If you're young and you get frequent dark-sky observing, 7x50, 8x56 or maybe 9x63 would be good. If you're more in an urban location and not as young as you used to be, then 8x40 or 8x42 or 10x50. If your sky is quite light-polluted, then 10x42 or 8x32 might be a very good choice. If your hands are very steady, you might like 12x50. A few people use as strong as 15x70 handheld some of the time, but remember that their field of view is smaller, things are harder to find.
Not sure what you mean by a "reasonable amount of money", but if you can afford up to $300 for the binoculars (not including tripod and mount), you can get some nice binoculars. Fully multicoated, BaK-4 prism models are recommended. In general, usually porro prism models are still recommended for astronomy.
If you will wear eyeglasses while using the binoculars, be sure to get plenty of eye relief, at least 17mm, in order to make sure that you really see the entire field of view.
Ed Cannon - Austin, Texas, USA