Here are some basic answers to your basic questions (anybody please feel free to correct or improve on these):
1) A great wave for surfing is any wave that breaks smoothly from one point to another in front of you, approximately parallel to the shore. Often you'll see waves like this where there is a point of land that protrudes out to sea. As the waves are deflected off of the point when they come in, they will tend to break away from the point. You don't want a wave that breaks at the same time all of the way across (known as a closeout), because there is nowhere to go once you catch it.
2) The dangers of surfing are relatively few, but they are serious and should be considered:
a. Above all else you should be reasonably fit, and able to swim a ways in choppy ocean water. It's possible for you to lose your board, even if you have a leash. Don't go beyond your limits, and don't underestimate the power of the ocean with its tides, currents and rocks.
b. Other surfers. There is a code of safety among surfers that I won't repeat here, but in essence it's your responsibility to watch out for other surfers and for them to watch out for you. Collisions and fin cuts can be nasty. Also occasional flying fists, if you're inconsiderate.
c. Sunburn and skin cancer, I suppose. Wear good waterproof sunscreen (like Bullfrog in the U.S.)
3) The part of the wave that pushes you when you're surfing is the shoulder right before the crashing, white part of the wave. Watch this point of the wave to see how it moves across either left or right. This is where you want to be. As you get better, you'll be able to surf on other parts of the wave (just watch somebody good), but you'll always return to this pocket to keep up your speed and position.
4) You should avoid conditions that are beyond your skill, fitness or safety. This includes waves that are too big, too far from shore for you to swim back, waves that break in dangerous conditions such as rocks or very shallow water. Also as a beginner, you should generally stick to beginner areas at your surf spots. It should become clear where these are as you watch before going in.
5) The characteristics of a good wave are generally described in 1 and 3. I suppose it should break for some distance and be smooth, but really any wave at all that gives you a memorable ride is a good wave.
6) A long board tends to maneuver more slowly, float more and work in almost any size wave. They're good for beginners because they are very stable and can catch even very small waves. A short board maneuvers quickly and is much more agile, but is harder to paddle and harder to catch small waves with.
Lastly, a few good sites to check out: