I started out using just one kind of colored pencils, now I use a variety of pencils to get a lot of different effects. Below are the list of current pencils I use, and what I use each one for. Note that you will probably end up buying some pencil colors more often then others so try to find a store that stocks them individually for re-filling holes in your set(s). Obviously these are not the only brands of colored pencils, so you may also find others you like as much or better.
Prismacolor Thick Lead Art
This is one of the most commonly used colored pencils. They are a waxy pencil and can be used to get very bright/solid colors. This is a good basic pencil to start with and excellent for "Burnishing". (Make sure to get their new "clear blender"!). These generally cost around $1 each in the USA. A good set to start with is the 40 pencil set, but you really want to end up with a full 120 color set eventually. These have a large variety of uses and are definitely a good place to start!
Prismacolor Verithin
Verithins are much less waxy and will hold a sharp point. These are good for doing details, often used in combination with Thick Lead Art pencils or Col-Erase pencils. These are not as well known as the first kind listed above and do not come in as many colors. They also cost about half as much and I usually I have to special order them (or order them online) because my local crafts store does not stock them.
Sanford Col-Erase
These pencils cost a LOT LESS then any of the others listed here. Only about $12 for a set of 24 when I got mine. First of all understand that they are not totally erasable and that if you do erase you probably do not want to use the erasers on the ends of the pencils. The great thing about these pencils is that they can be blended really smoothly! So with only 24 colors you can get a lot of different colors! Plus they erase well enough that you can put highlights into pictures after adding the basic colors. For blending large areas I suggest cotton or a tissue, for some areas stubs (AKA tortillons) work best. These pencils work great by themselves for a very soft, light colored look (it is hard to get dark or bright colors). They work really well to create backgrounds or in combination with brighter pencils.
Staedtler Karat Watercolor
As far as watercolor pencils go I have tried very few brands, so I am not an expert. I do like these pencils though! Most of the time I use them WITHOUT water! They are a very "heavy" pencil and work well for laying in solid shading or darkening colors. I often use them in combination with Col-erase pencils for some very interesting effects.
Derwent Artists Pencils
I started getting these recently - they are another of the more well known brands. These are much softer/chalky then the Prismacolors, but I like them for certain effects. More will be added on these when I have used them more.