Welcome to the forum. This sure is an old post brought back to life.
Let me give you my experience using stretch material. I started using Lycra and found it to be excellent for making bracelets. I was making them for selling at bizzars, I was buying the Lycra in 5000 yard rolls. I found that by doubling the strand and using a big eye needle and 3mm to 8mm beads the Lycra worked very well. I always used a surgeons knot and Hypo cement, pulling the knot inside a bead. After the bracelet was finished I pulled it out to at least twice the length. If it did not break it was ready to sell. Sometimes a sharp edge on a bead will cut the Lycra, but not very often. The sharp bead needed to be removed and reamed out. Crystals do not too well, too many sharp edges.
You can find how to make a Surgeon's knot by doing a web search for a diagram.
Etsy.com/shop/buttonsandshanks 100's of buttons
For stringing I like to use beading wire and crimp tubes/beads. You won't have to tie anything or glue anything. I don't really use stretch cord unless the piece has to be stretchy.
marutibeads.com - some really cool beads..
May I just say I hate elastic, but it is more of a one size fits all and older people prefer putting it on and off, so I can be forced to do it upon occasion.
The other posts all gave excellent advice. The only thing I would add is . . .
No matter what line I am using I never cut the line first. Not only are you wasting line, but if the line falls you only have a chance of the beads falling off from one end instead of two. Tip: If you do feel it falling, instead of trying to grab it and most likely missing or grabbing at the wrong point and the beads falling off, let the beads slide down the line so you have room on the line and if you do feel it falling, let go immediately. You have a much better chance of the beads not falling off the line.
When you get to the end, stretch the elastic a little before tying your knot so the bracelet doesn't slouch or is too loose. You can tie the knot without cutting it from the roll saving you elastic. After you tie the knot, hold the "tails" of the knot, and slide it into the bead with the biggest hole. Now cut your roll from the bracelet, leaving a short tail on the knot. If it's easier for you to tie the knot, cut it off the roll before you tie your knot. Take your GS Hypo Cement, gently pull one tail at a time and fill the hole and then release the tail. Do the second hole. Do not cut off the tails. Let it dry for 24 hours if you can, and then snip off the tails.
The elastic may break, but you will never lose a knot again.
GS Hypo cement is the only glue I would ever use on elastic. The others, super glue and finger nail polish have chemicals that will degrade the elastic. Also, tell people to not put alcohol, perfume, lotion, etc. on while wearing the elastic bracelet. In fact, they will last longer if they take them off when they wash their hands. If you take moisture and mix it with perspiration it will get inside the beads and further degrade the elastic.
I really do hate elastic. I don't even like wearing it.
Tip: To stop metal findings from tarnishing store in a ZIP Lock bag with a chunk of chalk.
A surgeons note is the following:
You have one of the cord, string, etc in your left hand and one in your right hand.
Go to tie it like a shoelace but do the following.
Left string on top, tie the two strings together.
The string that is now in you left hand make sure it is on top when you tie the two strings together.
Now make sure the string in your right hand is on top - and tie the two strings together.
So it's Left over, Left over, Right over.
Put the glue/polish on it and hide it in a bead or spacer depending on your design (so make sure you tie the knot next to the piece you want to hide it in.)