Pencil eraser: ask for a "putty rubber" at an art shop. I think the last one I bought was Windsor & Newton. They do go hard and crumbly after a while, but you can cut them in half and put the unused bit in a plastic bag. I reckon they'll keep for a year or so after which they lose their usefulness and do smear.
Also, always use a soft pencil - 3B probably. You can quickly sharpen it to a point or a chisel edge, but you want it to mark the surface with the graphite, not make a groove. That way it's easily removed as it isn't forced between the fibres. A hard pencil doesn't make a finer line, it just wears more slowly.
I do use hard pencils for rough work, but for anything that needs to be <0.5mm accurate, either a sharp, soft pencil or a knife (edge of pencil mark on the dimension needed).
My preference is 4B for fine work, 2B at the hardest. Trad carpenters' pencils are OK if you have the patience to sharpen them, but I find they don't sit well behind the ear, and if I put them on the bench they get lost, and it's a PITA getting that chisel edge just so and keeping it that way.
I have found the sanding belt cleaning crepe also works as an eraser (cut off a clean corner with a knife), but not as well. You can also lift graphite off a wood surface with cotton wool dampened with meths or xylene - best as the final clean up after you've used a putty rubber.