If you are completely new to watches, than the best thing to learn is the difference between mechanical and quartz watches (If you don't know already

).
A mechanical watch uses gears to keep time. You either manually wind the crown (the thing sticking out of the case, usually by the 3 or 4 o'clock position) or buy a weight that swings back and forth when your arm moves. Most are powered by swinging weights, and will usually be described as a hand winding watch if it isn't.
Quartz is just a fancy term for battery operated. Every couple of years or so they will need to be replaced, but other than that, you have nothing to worry about.
Quartz watches are usually more accurate, because there are no moving parts. That's not to say that mechanicals are extremely inaccurate. High end watches can lose only a couple of seconds every month, lower end ones will obviously not do as well. I lost about 20 seconds a day with my Seiko SNK807.
Mechanicals
Seikos are highly recommended for low cost and beginners watches. I started with the same model that Texas posted, except it was the blue version.
Another popular brand is Citizen, but they are a little more expensive. Most are over $100.
Another brand is Vostok. They are a Russian brand that some like, I personally think that most of their watches are ugly.
Quartz
I don't know many quartz watches. Casio is a very respectable brand. Timex is also another good brand.
Try some watch forums for more info. Most people on there are going to point you to the Seiko that Texas posted, but you can always try.
Good Luck! - Kris