"Invisible thread" is pretty good stuff for rigging under some circumstances. It's fine enough and has a really smooth texture. Its big drawback is that it's springy. It comes on a spool, and has a tendency to assume a curve unless it's under tension.
In practical terms, that means it's ok for ship rigging IF it's firmly fastened at both ends. To make it work right you really have to be able to secure one end firmly, let the adhesive dry, then stretch it to reach the other end point, secure it there, let that adhesive dry, and cut off the excess. For something like the rigging between the wings of a biplane, that works fine: you can drill holes for the thread to go through. For a small-scale ship, it's tougher. Putting enough stress on the thread to straighten it is likely to pull a mast or yardarm out of line.
There's no reason why several materials can't be used on the same model. For a long line running, for instance, from the foremast to the ship's bow, you might start by super-gluing a piece of invisible thread to the mast. Then pull it through a hole in the deck at the bow, put a drop of superglue on the underside of the deck (where it won't be visible), and cut off the excess. For shorter lines, such as signal halyards, you could use wire or stretched sprue. Cut them to length in advance, dip each end in white glue, and put them in place with tweezers.
One other thought. Most masts and yardarms in 1/700 scale kits are over scale. The most recent kits are much better in this respect than the older ones, but if a mast is reproduced to scale in styrene it's mighty fragile. Particularly if you're going to add rigging, it's an excellent idea to replace the masts and yardarms with brass wire. I like to solder mine together, but if you're not handy with a soldering iron you can use super glue. You'll find the brass masts are much stiffer - and if they get bumped by accident they bend, rather than break.
Hope this helps a little. Good luck.
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