I can see Saturn's rings with my 16x70mm binoculars. Jupiter's Galilean satellites are easy with any decent pair of binoculars. You can track their positions relative to Jupiter from night to night.
Binoculars are definitely the way to go for a beginner. Spend 12 months using the naked eye and binoculars to learn the entire night sky that's visible from your location. With the aid of an astronomy book and star charts, you'll learn all the constellations and the names of the major stars in each, plus other interesting objects in each constellation (Messier objects, variable stars). Binoculars also bring out the different colours of many stars. Supplement this with background reading on the targets of your observations and other nearby objects.
During this time, you'll also be able to learn many of the most prominent features of the moon's surface, as well as easily being able to identify the planets (although Mercury can be a challenge and Neptune requires large binoculars and even then will just be a speck of light), and you'll get a feel for which constellations are visible in which seasons. Learning the sky like this is very satisfying and is a great precursor to buying a telescope. Your binoculars can of course be used for other purposes too.
As casual astronomers are generally most interested in the moon and planets, I'd recommend buying a medium-sized apochromatic refractor as a first scope. A high-quality 4" (100mm) one with a good mount can be had for under $1000, and will give stunning views of Saturn, Jupiter and the Moon, even in the middle of a large city. Other planets and the brighter star clusters and nebulae will also look good.
Unfortunately, the pairs that I have are all no longer produced. If I was in the market today, I'd probably look on Craigslist for some high-quality second hand binoculars. That way, you can go and test them in person after you've researched them online, and you should be able to get more for your money compared with buying a new pair.
For astronomy, you want a large objective lens:magnification ratio, because the higher the magnification, the dimmer the view. For daytime use, this doesn't matter, but for looking at faint objects at night, light-gathering power is everything. Get this ratio at least up around 5, or ideally 7, so 7x50mm binoculars would therefore be better (and lighter) than 10x50mm. I'd start with those before possibly getting some larger (e.g. 15-16x70mm) ones, or just moving straight to a telescope.
Binoculars are definitely the way to go for a beginner. Spend 12 months using the naked eye and binoculars to learn the entire night sky that's visible from your location. With the aid of an astronomy book and star charts, you'll learn all the constellations and the names of the major stars in each, plus other interesting objects in each constellation (Messier objects, variable stars). Binoculars also bring out the different colours of many stars. Supplement this with background reading on the targets of your observations and other nearby objects.
During this time, you'll also be able to learn many of the most prominent features of the moon's surface, as well as easily being able to identify the planets (although Mercury can be a challenge and Neptune requires large binoculars and even then will just be a speck of light), and you'll get a feel for which constellations are visible in which seasons. Learning the sky like this is very satisfying and is a great precursor to buying a telescope. Your binoculars can of course be used for other purposes too.
As casual astronomers are generally most interested in the moon and planets, I'd recommend buying a medium-sized apochromatic refractor as a first scope. A high-quality 4" (100mm) one with a good mount can be had for under $1000, and will give stunning views of Saturn, Jupiter and the Moon, even in the middle of a large city. Other planets and the brighter star clusters and nebulae will also look good.