Wow! Quilt as you go is pretty complicated for a beginner. I would probably start with a smaller item to be able to learn the fundamental techniques before trying to tackle the quilt you've described. In addition to the complicated instructions, the other thing you have to watch out for is what size your seams will be when you're adding the next piece. When piecing at top, seams are a scant 1/4" (roughly 3/16"). However, with QAYG, you have to make an allowance for the batting and up to 3 layers of fabric. There isn't a hard and fast rule in that case -- it will depend on the loft of your batting.
Okay, that said, if you are really up for a pretty good challenge, you are correct about how to do the layers when adding the sashing/next piece. Straight lines in the sashing would be acceptable, or if your sashing is 2" or less, you don't need to quilt it at all (the QAYG method will provide quilting lines at each of the seams, which is sufficient as long as it's not wider than 2"). As a point of clarification, you want to be sure to quilt the blocks before adding the sashing. The main thing with the corner squares is that you probably are sewing on the bias. To make things a bit easier on yourself, you can glue baste those seams (just mix together a bit of Elmer's washable glue and enough water to make it thinner but not watery in a Dixie cup) -- you just dab a bit with your finger/flat toothpick/paintbrush along the edges you plan to sew together & then iron to dry the glue. That way you won't have to worry about the bias edge shifting on you.
All that said, I really would encourage maybe choosing a smaller, more traditional project for your first quilt. A table runner, placemats, pet quilt, crib quilt or lap quilt are all good choices. Picking a pattern that uses squares, rectangles, half square triangles or some combination thereof would be good options to begin to learn piecing. Straight lines that can be quilted with a Walking Foot (or if you have a Dual Feed machine) are a good choice for beginning quilting.