You want to SID no matter what to make sure that it really lays flat. If you pick a 50/2 mid-grey (lighter than the paisley diamond in center of pineapples, darker than the light grey floral) it should be basically invisible.
I'm assuming you're asking because you want something more than SID. SID would certainly be an option, but here's another option for you to consider.
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For the pineapple blocks, I'd stick with a 40 or 50wt mid-grey thread so it does not show up very much and the piecing can be the focus. I'd do one small "star" in the very center square & then two more echoing that, touching each of the paisley pieces. I'd do triangles in a 40wt mid-grey. I would not hop to the outside of the white line until I reached within the 1/4" of the border that my binding would cover. Then I'd "continue" (minus the white) the lines from the triangles out to the edge of the quilt & follow back in to the white, travel stitching to next angled line.
When all of that was done, I'd consider adding a motif in the center of each "block" that was formed by your crossing lines. As a beginning FMQ'er, I'd recommend grabbing some scrap fabric to practice first, but doing a simple 4-petal motif (marked with white pencil or Ultra Clean crayon) in a 50/2 thread that is the same blue as the background would be simple enough & the thin matching thread would allow any minor glitches to seamlessly blend in. You need a Darning foot (also called Free Motion foot) to do FMQ on a domestic machine. It could also be done on the Sweet 16, but that isn't necessary as long as you have a Darning foot for your regular machine.
I would definitely mark your design first, especially as you are on a tight deadline.
As for the binding, speaking from experience, doing a "regular" double fold French binding is FAR easier than self-binding. The only reason I'd suggest a self-binding is if you are short on fabric. I did self-binding once. It took me hours to get the corners even close to decent. I would never do that again.
Last edited by Bree123; 07-31-2016 at 07:15 PM.