Sounds like you might have found a piece of silk charmeuse based on your description. You should treat your fabric the way you plan to treat your garment. I have no qualms sending my silk crepe de chine or charmeuse pieces through the delicate/lingerie cycle of my washing machine, or washing it by hand. I then flat or hang to dry. Some silks will water mark if they get wet, always do a test on a scrap piece before any kind of treatment.
I am partial to natural fiber thread on all of my projects, using mostly cotton or silk threads but they are not as strong as polyester or a poly blend. This link that I am going to share suggests using poly thread, so it's really up to you.
You are probably going to find that cutting charmeuse is going to be a PITA! You can use spray starch on it to make it less slippery when cutting, but be sure to test a scrap piece so you're sure it will not damage the silk and/or it will all be able to wash out. Another trick is putting a piece of paper underneath the fabric when cutting to prevent slippage.
Storage wise, keep it away from direct sunlight. I store my fabrics in a plastic tupperware box, only after they are wrapped in a cotton sheet. I'm not sure if moths like to eat silk like they do wool, so if long term storage is what you are looking for, I'd go with a plastic box instead of a cardboard or fabric container. Just be sure it is away from direct sunlight!http://www.craftstylish.com/item/918/more-tips-and-tricks-sewing-with-silk