I use the ArtBin plastic ones with a handle. Numerous places have them but watch the price as they vary quite a bit from store to store. JoAnn's carries them but their regular price is really high so use a coupon or wait until they put them on sale. I've seen them at Hobby Lobby, Michael's as well.
At guild we made a carrier to keep quilt blocks in progress. It used a paper towel cardboard tube as a base on one end. You took two pieces of fabric cut in a rectangle and stitch them together leaving room to turn the fabric right side out and also insert the cardboard tube. Stitch a line down to secure the tube. Attach some ribbon on the other end and then you lay your quilt block flat on the rectangle and then roll it up around the tube and tie. It keeps your blocks neatly rolled around the tube until you are ready to assemble the quilt. I didn't make one but perhaps someone out there has made something similar and could post a picture or better directions. I have my box so use that but when you transport your box things do slide around and you have to rearrange your blocks to set them straight again.