I almost always work on a single piecing project at a time. In my mind, piecing and quilting are two separate activities, so completed tops are not UFOs, they are completed tops!
Anyway, I find that I'm most effective if I work on a single task until it's done. The only exception is I usually make a one of sample block. Generally, this is how I approach the rest of the quilt: After the sample, I cut all the pieces for the quilt blocks. I don't cut the sashing or borders. Then I analyze the blocks and break the construction down to specific tasks. So maybe I'll do all the HSTs, sewing them all, then pressing them all and squaring them all. Then do all the 9 patches, again sewing pressing and squaring till they are all done. When I have the sub units done, I'll start constructing the blocks. I put the blocks on my design wall and decide if I want sashing or not. If I do, I cut all the sashing and add it to the blocks (I prefer sashing the individual blocks). Then join the blocks. Audition the border fabric(s) then cut & apply.
There are exceptions, for instance scrappy quilts. I prefer a controlled scrappy, so I might cut everything, then arrange all the pieces for an individual block, choosing specific colors or fabrics. Once selected, I use paper plates to keep the blocks together. In this case, I might work on one or two blocks at a time completing them individually.