The line chosen depends on many variables: the style of the necklace is only one of them. A very important one, indeed.

I use chains and wires of various metals (silver, gold, steel, etc) leather thongs, different textile threads (cotton and hemp my favorites, either single or several threads together, braided or not).
Depending on the project, industrial materials may be of use as well: electrical plastic-coated copper wire (why not?),(not-nylon) fishing line*, etc.
Sometimes it may be advisable to use different types of line in different places of the same necklace -- i.e. springly wire to string the beads, with a leather thong or a vegetable fiber braid tied at the ends of it, to finish the back of the necklace with a sliding device, in the traditional size-adjustable Indian style.**
*Beware, some of these, specially those too resilient, may be dangerous: wires, or cords used in ships, could seriously cut flesh in the event of the necklace getting hooked somewhere. A "security point" should be there, for the thing to break just in case.
**I could show several cases/images with different solutions chosen, if required.

But of course, more than anything else, the critical point is the size(s) of perforations. There are many tricks to reduce the gauge of a perforation, the problem is generally the need to enlarge it, and the possibility or convenience of doing this: i.e. when you do not want, or dare, to change an ancient bead.

In the necklace shown here the case is rather complex: the lapis beads have a confortable 2 mm gauge hole; the modern gold-and-ruby discs have a 1,3 mm perforation, which could be enlarged to some extent if needed; the ruby beads have a small hole and, although very hard, could also be enlarged at will; now, the tiny old Basra pearls are extremely fragile and their perforations are not much larger that 0,3 mmm.
Not easy to decide.
So this necklace is strung on nylon coated stainless steel wire (0,3 mm), which I consider to be for cultural and practical reasons (it bends and stays at an angle, or breaks suddenly after some time) only a temporary emergency expedient...although perhaps it is less temporary than hoped for, as happens all the time in society at large.