There are several different brand names of art paper and most of them are good quality. Typically, I use Bristol Vellum by Strathmore. It's a heavy weight paper and has a nice texture. The pads of Bristol Vellum that are commonly found in art supply stores come in sizes of 9" x 12", 11" x 14", 14" x 17", and 19" x 24". I am making a larger drawing for this demonstration, so I will be using a Canson brand illustration board that measures 30" x 40".
Pencils: As with art paper, there are many different brand names of colored drawing pencils. After years of experimenting, I have found that the Prismacolor brand is my favorite. They are soft enough to blend well with each other and have rich color. For the beginner, I would suggest buying an assortment box that has a wide variety of colors. Colored pencils may be purchased individually, but you would have to know exactly what colors you need, and typically the individual cost per pencil is less when buying an assortment. In my case, I have been drawing with Prismacolor pencils for decades and have amassed quite a large selection. For this illustration, I will name each color as I use it.
In order to choose the correct colors for various projects, I observe each separate colored area in the photo, compare that to the colors I have available, and then purchase additional colors, if necessary. For example, when selecting the colors to be used for a typical sky, I gather all of my variety of blue pencils, color small squares on a scrap piece of the same type of drawing paper I am going to use, and then hold those samples next to the reference photo. From those samples, I select the pencils that reflect the various shades which I want to reproduce from the photo onto my drawing. You should never rely on the color of the pencil from it's outward appearance.
I also use a soft graphite pencil to lightly sketch guide lines for my illustration. I don't use an extremely soft pencil because the lines would smudge easily; whereas a pencil that is too hard will produce a lighter image which can make the guide lines difficult to see. A number 2B pencil works best for me.
Graphite Stick: Graphite sticks are basically large flat pencils without the surrounding wood casing. This is a useful tool to fill in large areas of graphite for transferring your image onto the drawing paper. They come in a range of hardness, but I prefer the 2B. A number 2 pencil can be used for this purpose, as well.
Erasers: Erasers will not work with colored pencils because they are wax based; however, you will need an eraser to remove your graphite pencil guide lines. A very soft eraser works best, to prevent the paper from being damaged or scratched. I use kneaded erasers which are extremely soft and flexible. They can be formed into tiny shapes to erase very small areas, and are cleaned by stretching and folding them.
Sharpener: Colored pencils work best when they are very sharp. (I'll explain in detail later why the pencils need to be sharp.) I highly recommend using an electric sharpener. Hand sharpeners do not work well because colored pencils are fairly soft and if the pencil is held at a slight angle while sharpening, the wax breaks very easily. It's extremely difficult to use a hand sharpener and keep the pencil perfectly straight. The only time I use a hand sharpener is when the pencil is too short to fit in my electric sharpener and I don't have a spare pencil of the same color to finish the area I'm working on. Sort of like using a roach clip.
Dusting Brush: An artist dusting brush is needed to lightly remove the extra pencil wax which forms when creating several layers of color. Using your hand is always a bad idea. Even a slight pressure from your hand on the dust can create little balls of wax which will draw lines on your paper as you rub your hand across. Using your breath to blow the dust off is not a good idea, either. Quite often, even if you are very careful,this can result in actually spitting on your paper. If you don't have an artist's brush....buy one.