If I use starch, I spray my yardage (or the amount I think I'll use) and press before I make the first cut. I like to give the fabric some substance, but not make it cardboard-stiff.
Sorry you're getting such divergent answers. Maybe you should try making a few of the same blocks, and skip the starch on one, starch before cutting on one, before sewing on one, etc. Then you could decide what works for you.
Regarding pressing vs. ironing, pressing only involves up and down motion of the iron. Ironing involves moving the iron around on the fabric, and can stretch or distort your fabric, creating problems later in the process. When you press, you only press one iron-shaped section of your fabric at a time, pick the iron up, and press another spot. It takes longer, but the accuracy is worth it.
Hope that helps,
Darren