Drawing Supplies

Erasers, Pencils, Pens, Paper

Unless you have a good art supply store near your home, you will have to buy on-line if you need something better than the items sold at big-box stores. I recommend 2 suppliers, Mr. Art and Dick Blick. I've purchased items from both companies. There are other suppliers that I am unaware of, so if you have a supplier that you are happy with, please do not feel like you have to switch. You do not [or may not] need every item that is listed.

I have scanned some of the things that we use.

Erasers

You will need erasers. The erasers that are shown in the image have been used on charcoal drawings.

I haven't opened my new kneaded eraser yet, but I have an old one that we use and it is not pictured.

The kneaded eraser picks up, not rubs off, and that means after a while, it becomes full. When the kneaded eraser makes marks instead of removing marks, it is time to replace it.

The children liked using the pen-type erasers, [also called tube eraser]

Pencils

You will discover a wide assortment of drawing pencils when you shop. The ones shown in the image are mostly charcoal pencils. There is often a number and letter on the charcoal and drawing pencils, look for the following when you buy: 
Charcoal: 6B, 4B, 2B, HB, 2H, or S, M, H

Drawing pencils:  Soft<-- 6B, 4B, 2B, HB, 2H, 4H -->hard. Experiment with your drawing pencils to see the range of shades each one is capable of.

Vine charcoal, soft and medium, do not buy hard

Compressed charcoal sticks: 2H [hard], HB [hard], 2B [medium], 4B [soft]

Conte crayons, get black or sanguine (reddish brown)

Ebony pencil- all are soft

Related: Shading Scale shows examples of pencil hardness in example.

Pencil sharpener, I know of pencil sharpener that I am comfortable recommending and that is this the aptly named- The Best Pencil Sharpener Ever

Pens

Calligraphy
I've not done calligraphy in ages and I am not familiar with current calligraphy supplies. In the past, I've used two types, the dip type in which the nib is dipped in a bottle of ink and the cartridge type in which the pen holds an ink cartridge.

Artists Pens
We use Faber-Castell PITT artist pens.

Paper

Drawing Journals
Journals differ greatly in quality. My daughter has used journals for several years and her favorite ones are the black hardbound books with smooth paper. She numbers her journals and is currently on #13. She uses them to graphically develop her cartoon characters, which includes sketches, notes, and color pallets for the characters.

Journals have different types and qualities of paper in them as well as being bound differently. The paper varies from being thick and rough to thinner and smooth. The thick rough paper is almost like drawing on construction paper and the smooth paper is like drawing on printer paper. Find out what type of paper your children prefer before buying a journal.

Drawing Pads
Two common paper sizes are 9" x 12" pads and 18" x 24." We use both sizes, the 9 x 12 size is used the most. The cover on the drawing pads usually describe the best use for the paper inside, such as watercolors, sketching, and pastels. Some labeled sketch pads also say "heavy enough for water media". Look for paper that is acid free and most of it is.

Other
If you use charcoal , you will need some spray fixative [clear].