Stringing and Beading:
When doing stringing projects, you will need a good quality beading wire. I have used Softflex for quite awhile. I trust that my jewelry won't break, and that it won't fray or get kinks in it. For most jewelry, I use the 21-strand, and for heavier beads, the 49-strand. There are other brands out there, but once you've used Softflex, I think you will discover the difference in the quality, and feel more confident about your jewelry not coming apart.
For knotting between pearls, or beads, Griffen silk beading thread with the needle attached is a good choice. Most knotters prefer this thread over the polyester thread, or the silk thread without the needle. It's a good idea to check the size of the thread against the size of the hole in the bead. There are a number of sizes, 0 to 12, and I found that if you are using real pearls, the hole is smaller than other beads. I like to use 4 or 6, but larger sizes probably won't go through the pearls.
If you want to use jewelry wire, like copper or sterling silver, 24 gauge, half-hard is the usual choice. There are also jewelry wires (non-sterling, non-tarnish, not expensive) that can look good, be strong, and not cost a fortune. Again, the size of the hole and the weight of the bead will determine which size wire to use. When hammering out your wire for bigger projects, like bracelets and pendants, the larger sizes of wire should be used. !6, 12, and even 10 can be a lot of fun to hammer and form, the smaller wire, like 26, 24, and even 22 can break if hammered too thin.
Elastic for stretchy bracelets is always popular. However, there is no strong elastic, it will eventually break, and your jewelry will have to be repaired or thrown out. I recommend elastic for children's jewelry, disabled, or for elderly people who have trouble with clasps. Never pull on your elastic jewelry, always carefully roll it on and off.
Leather, pleather, rubber, cotton, and other cords are available for jewelry-making. There are special crimp ends for these materials, and there are a variety of sizes. Check the size of the hole of the bead before purchasing your cord, to be sure that it can pass through the bead.