The reed is possibly the most important part of the saxophone. Without a reed, there would be no sound. When you blow into the sax, the reed vibrates and creates sound. Using your fingers, you can cover different combinations of holes to get the desired note. The better the mouthpiece, the better the sound, so if you plan on playing for a good long time it would be worth the money to purchase a quality mouthpiece. For beginners, though, a student mouthpiece will serve the purpose just fine.
Now, how to choose a reed. Reeds range in sizes from 1 to 5, with 1 being the weakest and easiest to play and 5 the strongest and hardest to use. The higher the reed size, the better the sound, despite the difficulty. Size 2 is about right for a beginner. As you continue to learn and practice, and 2.5 will make a considerable difference.
I would have to say that Rico Reeds are the most popular, effective and least expensive choice. They make a variety of different types, including the Rico Royal. These are specially designed and French cut in a way to make articulating as easy as possible. I would say, from experience and research alike, that Rico Royal reeds are the best choice for a beginner. For a list of all reed types and when to use them, go to Rico Reeds.