I wish the subject were that simple, but I'm afraid it isn't. There's quite a bit of debate among ship modelers as to what the best rigging material is.
I happen to like silk myself. Nowadays, however, it's hard to find - and next to impossible to find in the wide range of sizes needed to do a serious rigging job on a good-sized model. A couple of sizes used to be available in good sewing stores. For my little model of the frigate Hancock I bought dozens of spools of the smaller size, and spun them up on my primitive "rope making machine" into the dozen or so necessary sizes. I don't think many plastic ship enthusiasts want to make their own rope. (I don't blame them; it's not particularly difficult, but it takes a lot of time.) And nowadays silk is awfully scarce. I haven't seen any in a sewing store for at least thirty years (in any form a ship modeler could use). I've googled "silk thread" several times on the web, but haven't found a source that sells it in more than one or two sizes. (If Tankerbuilder knows of such a source, I'd be mighty happy to hear about it.)
Fly-tying specialists sell a few sizes and colors of silk, and it's beautiful stuff. It's also extremely thin. It's great for 1/350 and even 1/700 warships, but not really practical for sailing ships on larger scales. And I once asked a surgeon if surgeons still used suture silk; his answer was yes, but it only comes in relatively short lengths pre-bonded to needles.
The old-timers were fond of linen thread, which, they claimed, was the only stuff that would last for generations. I have my doubts about that,but good genuine linen is nice stuff all right. Bluejacket ( www.bluejacketinc.com ) sells several sizes of it, and it's certainly good stuff - but the range of sizes is limited and it only comes in white. You have to dye it yourself - and the dye injects its own problems of longevity.
About the only real rule I can suggest is: don't use cotton. It's flabby, disagreeable stuff, and is extremely hygroscopic - it shrinks and stretches, fast, with changes in the humidity. If you do have to use cotton thread for some reason, for heaven's sake follow Tankerbuilder's advice and wax it. (Unless you get some really fuzzy stuff, waxing shouldn't be necessary with silk or linen.)
Model Expo used to sell a big variety of sizes, and several good colors, of what it called "cotton-poly mix." I've rigged a couple of models with it, and really like it; it genuinely looks like scale rope. But lately the number of sizesand colors has shrunk a lot. A small firm called Cottage Industry Models sells something similar. It's not cheap, but it looks great. I've got an assortment of it on hand, though I haven't had a chance to try it out in any quantity yet. One great feature: Cottage Industry offers to make it in either right-or left-hand twist. (For a ship built before about 1815, you want lefthand twist, aka cable-laid, for the shrouds and stays, and right-hand - aka hawser-laid - for most other lines. For later ships, you want hawser-laid line everyplace.)
Bluejacket also sells nylon in quite a few sizes - all white. At least one famous ship modeler, the late Harold Hahn, used nylon almost exclusively for rigging. But he just bought the smallest size he could get, and spun it up on his rope making machine (which made mine look like a crude toy). The larger diameters, to my eye, don't look much like rope.
If I were tackling one of the big Revell or Heller kits, I'd probably buy linen from Bluejacket or the cotton-poly stuff from Cottage Industry. One big bottom line: don't expect your local sewing store or arts and crafts store to help much.
I'm sorry to make a seemingly simple topic so complicated - but I'm afraid I can't do anything about that.