I am in the process of moving. I used clear trash bags for my fabric because I want to refold it into those neat all one size pieces that someone did a tutorial for a while back and this will make me do it as I put it on the shelves.
I bought a lot of the Uhaul boxes figuring they'd know how to make a packing box. I won't discuss my opinion of the quality of those boxes. You're better off with a sturdier box especially if you're packing anything that has any weight to it. Or that you care about, especially if someone else is going to be tossing those boxes around.
Be careful packing books, they are HEAVY. I filled a small box (about 9x12x12) with books and tried to take it downstairs but ended up having to wait and have DH do it.
A really nice box to pack things is the kind that printer paper comes in. They're strong, they stack great and are almost indestructible. You can pack folded fabric in them really well. Kinko's has them and can sometimes save some for you, or Staple's.