For a lightweight quilt, I purchase the thin light weight fleece that Walmart carries and use that for the batting. It's up to 60" wide (check width before buying though), so if your quilts are going to be less than 60 inches wide, it works well. You also don't have to worry about it bunching up in the case that you didn't tie or quilt it close enough together.
I'm not sure if cross-grain and length-wise grain terms apply to knits, though, so will suggest that you determine which direction the fleece is least stretchy and put it in the quilt sandwich so as to have the LEAST stretch in the fleece when quilting or tying. I almost always spray or pin baste when using the light weight fleece as batting as it tends to be slippery when quilting, especially if it's not being quilted on a frame.