Bristol board is my usual choice for drawing on paper; there is nothing really special about it, but it works well. I usually buy Strathmore brand, with the so-called vellum surface. Which is really nothing like an actual calfskin vellum surface.
I use handmade cotton paper for many printing projects, and occasionally draw on it also. I buy mine from Twinrocker Handmade Papers in Brookston, IN, one of the last paper mills making real laid paper. Laid paper has a slight ribbed texture because of the way the wires are arranged in the papermaking mould; there are many thin wires running in one direction, and more widely spaced wires perpendicular to these. You can see the evidence of these when you hold the paper up to a light. (This piece also has the Twinrocker watermark.) Laid paper was the only kind of paper available in Europe before wove paper was invented in the 18th century. I rather like the way it feels and prefer it for my own medieval-styled artwork.
Certain other paper mills sell fake laid paper that has the texture impressed into it by a mechanical roll at a late stage of the manufacturing process. This rather offends me.
As a drawing surface, handmade paper is not a precise as Bristol board, calfskin or goatskin, but it has an appeal of its own.
Graph paper is useful on occasion. Drafting vellum is a translucent plasticky film that I use for tracing and transferring images. I don’t like that this, too, is labeled vellum, because to me vellum means calfskin, not Bristol board and certainly not plastic film.
Draftng vellum is nearly impossible to tear by hand, and this is the other reason I keep it nearby - whole sheets of this are great to give to babies who like to play with paper!