Wax-based pencils are recommended when you want to do a lot of layering or blending. The color flows onto the page smoothly and easily, allowing for a great deal of expression in the line and tone of your work. The major drawback to these types of pencils is wax bloom. This is a whitish haze that develops over the surface of the artwork as the wax in the color rises to the surface. Artist David Deen provides good tips for how to deal with this issue such as wiping the surface with a cotton ball or spraying it with a fixative.
Oil-based colored pencils also contain some element of wax, but not to the same degree. They tend to be harder and require greater pressure to apply the same amount of color. They also tend to bleed easier and can be lifted with water. Blending is accomplished with turpentine as compared to the odorless alcohol used with wax pencils. As is pointed out in Designed by Kristi, these properties make it more suitable to working on wood or similar surfaces.
Watercolor pencils can be wax or oil-based, but artist Gary Greene explains they are created with special emulsifiers included in the lead so that the color liquifies when water is added. This enables you to create an effect very similar to watercolor while retaining greater control over color placement. Another advantage of colored pencils is that all of these different types of pencils can be used in any combination, enabling tremendous flexibility in expression and execution.
If you are confident in your artistic ability in another medium, you will get better results with a better quality set of colored pencils. However, if you are just starting out, those Crayolas in the back-to-school aisle will give you a strong introduction and a nice feel for what a colored pencil can do. Tiffany Grey points out "student grade colored pencils (such as Crayola, Rose Art, Prang) are very different from artist quality pencils." Artist quality brands include Bruynzeel, Faber-Castel, Schwan-Stabilo and Prismacolor.
There are a number of other supplies that can make your colored pencil project more successful. These include:
Erasers - electric eraser, kneaded eraser, eraser shield, pink eraser, tape, solvents are some of the options for removing color from your page
Pencil sharpener - several ways to bring a point to your pencil include a knife, a traditional hand sharpener, electric sharpeners or even sandpaper
Blenders - these can be stumps, tortillon, tissues, brushes, cotton swabs or even your finger.