I used Spider’s Web (Ben Goldberger) model to test a sheet of paper which is sold by IKEA under the name Givande and which I got my hands on courtesy of Aleksander Biestek. It is sold as a gift-wrapping paper and it feels like a thin Kraft paper. It is black on one side and a natural brown on the other [update: black seems to be out of stock as of 2021 and only natural brown is available], though without the striping typical for Kraft paper.
Precreasing, including reversing the creases, went well. Black paint did not come off the folded creases, as happens with some painted papers, and since good black papers are hard to come by, this alone makes this one worth evaluating. Thinness made it possible to fold quite precisely. This model does not challenge the paper’s strength too much, so it’s hard to tell if it would tear after lots of precreasing or under higher tension.
So, this paper has many good properties, but apparently it was not such a good choice for this particular model. The reason is that it does not hold the crease too well, and the web in this model has some folds which are rather loosely locked. Therefore, for folding this particular model, I would now choose a thicker, more sturdy paper. Still, I think Givande has a lot of potential, and, for example, for a pure square twist tessellation, it would have been OK since in such a model all pleats are tightly locked and holding the crease is not as important a paper property. It may also be a good choice for many figurative models.