The line MicroMark sells is described as "cotton with a hard finish" - presumably some sort of coating. It looks excellent in the pictures. Experienced ship modelers generally shy away from cotton; it tends to be flimsy, fuzzy, flabby stuff, and is reputed not to hold up well. It also seems to react more to changes in humidity than either silk or linen, but I'm not sure there's actual evidence to confirm that. If MicroMark's supplier has found a way to eliminate the fuzz, the same coating may take care of the humidity problem and it may well be a nice material. My biggest reservation about it is that, at least in the catalog I've got, it only comes in two sizes.
The preferred rigging material among the veterans is, and has been for years, linen. Those there are who claim that linen is the only fabric that really lasts. On the basis of what I've seen personally, I think they're mistaken. When I was working at the Mariners' Museum I worked on quite a number of old models whose rigging was made of lots of materials, and I couldn't detect any consistent patterns of deterioration. The linen rigging of the famous Crabtree models, for instance, was showing its age pretty clearly; some lines were on the verge of snapping, particularly at spots where they ran through fittings that were made out of acidic woods, or where drops of varnish had been splashed on them. On the other hand, the cotton and silk rigging of some other models of similar age looked as good as new. On the other hand, some old silk thread that I've seen has snapped on a gentle yank. In my opinion atmospheric conditions and the care a model receives are far more important to its longevity than the rigging material. If you find some cotton thread that looks like real rope, and is the right diameter, I say - use it.
My own preference for a long time, as I indicated earlier, has been silk. I've got evidence in my living room that a model rigged with silk thread, kept in a plexiglas case in reasonably well controlled temperature and humidity conditions, can easily last 28 years. (I finished my little H.M.S. Bounty in 1978, and its silk rigging literally looks as good as new.) Lots of modelers have reservations about synthetic fibers, because they haven't had time to demonstrate their longevity. But Harold Hahn, one of the best in the business, uses nylon line exclusively in his models, and I've never heard that any of his rigging has disintegrated. If modelers want to lie awake at night worrying about whether their rigging will last 200 years or fall apart after 100, that's their privilege; personally I have other things to occupy my mind.
I would have reservations about mixing rigging materials on a model, for fear that changes in humidity might make different lines react differently. Otherwise, though, my personal approach is to use whatever material looks and handles best.