I would use
49-strand Beadalon or
49-strand Soft Touch Soft Flex. Usually, .018 - .019" diameter works well with gemstones, but for very small stones you might need .015" or thinner. Heavier diameter is stronger, so use the heavier size if you can.
Finish with crimp beads and (optional) bullion wire or (optional) wire protectors. (To see which finishing methods/products work for the style of beading cable you're looking at, click into the product's details and scroll down a bit for more info.)