I have pets of every possible fur color but amazingly even the black fur shows on black fabric. It's the main reason I don't like working with flannel (black or not), all I have to do is walk from one end of the house to the other and the piece will attract fibers and hair like a black hole...
I find a smooth weave with a slightly shiny appearance is best for me, coarser fabrics seems to have the fur/threads line up with the weave and be harder to get off than those cross-wise. I decided a few years ago that I would only buy Kona Black so that all my black scraps are consistent. Hate having some blacks not as black as others, especially when you have a lot of black background it can really show.
I use all the standards, blue tape, lint rollers, and when it is really bad (like if somehow the cat gets on top of it and sleeps on it, a slightly damp washcloth and vigorous scrubbing motions.