Longaberger baskets are what you want!! I have two with lids and handles that I use for keeping my sewing items (scissors, pins, needles, fabric, etc.) in them. I keep one next to my chair in the living room. One is medium, and one is larger, but not too large at all - not like a picnic basket, more like purse sizes. They are kind of expensive, but they are so worth it. Go here and you will see the one I bought for $54, 5th row down, 1st in row. Mine have handles on them. If you click on that one and go to the bottom of the page, you will see some more with handles on them. I'm not sure if that one has handles. It doesn't look like it does. You would definitely want handles. Two handles usually. They are awesome for what you want to use them for!!
http://www.ebay.com/sch/Baskets-/39612/i.html
Just type in: Longaberger baskets with lids and handles in ebay's search bar and a few will show up. The middle one in the top row is similar to the ones I have. They are not lined, but being a quilter, you could line it if you need to. I like mine fine without being lined. And then there is Amazon to check out. But Longaberger is high quality baskets! That's what you want. They are like Amish type baskets. Made very durable! I've had mine for years and years and they are perfect still! You could type in 'Longaberger baskets with lids and handles for sale' in the Google search engine and probably find lots of them. Sorry this is so long. I became so excited that I was able to share about these baskets!