I'm in the process of winding mine on plastic bobbins right now. I may be a bit ocd about it tho. I actually cut them to length and then wind each length onto the bobbin. That was the one thing I always hated about storing it on bobbins, you'd end up with weird lengths of floss to work with.
I also cut the number from the wrapper and tape it onto the bobbin so I can see it in the storage box. I tried the labels once but they fell off. I figured if I was going to tape something on it anyway, why not use the wrapper from the skein??
I put mine on bobbins in a box sorted by number.. I have one box that all my bobbin boxes fit into so that it is easy to keep them all in one place together.
I keep my mouline threads each separately in a bag in a box divided into colors. Those that I use on a regular basis keep a smaller box. I do not want to waste time winding them on bobins.
I have all my skeins on bobbins and the extra skeins I have in a big plastic bag. When I do a project I take all the colors I need and put them in one box so that I don't need to go over the 5 boxs to find the right color. And Thats a great idea to put a list in the bags with all the Numbers on it. I think i might do that too I got so many extra floss now I have to take all of them out to see if I have a certain number . I'm making a list now thanks for the idea.
I wind all my cottons onto bobbins and store them in floss boxes and just take out the cottons i need for each project. I find this works great for me and is quick.
I personally prefer to keep the thread on bobbins and keep all of them into boxes according to the numbers. I have seen people keep the thread on paper plate like DIM thread organizer according to continuous thread number.