These are the different charcoals I use, you won't find willow or vine charcoal here as I don't use it in my style of work. I prefer the darker, heavier charcoals such as the pencils and compressed sticks, and my favourite pencil brand is General's in a 2B. I've never had any problems sharpening them or finding hard bits in them.
I use the charcoal powder for backgrounds and the white charcoal pencil for highlights.
I really only use one main paper for my charcoal drawings which is a watercolour paper, Arches Hot Pressed. I love the hot pressed because it is smooth and i like the feel of how the charcoal goes onto it. It is also good for blending the charcoal powder background. I have also used smooth matt board, yep that's right, matt board that you frame with. It is archival and a great way to get a mid tone colour background. Another one that I have been told about but haven't used yet is Colourfix Smooth Pastel Paper. Apparently this is a great charcoal paper which I will be trying myself soon.
I've listed here additional items that I use in my art practice. I highly recommend the Caran D'ache Grafwood pencils for graphite drawings.
Scale Tool for drawing in proportions. A must have if your learning how to draw freehand.