For a pantograph, I'd go with a thread that is 1-2 shades darker than the tan in your piecing.
If you go with red, the quilting will be the only thing you see. The only time people will notice the piecing will be if they think it clashes.
Navy will only show up in the floral squares & on the red border, so unless your design fits perfectly inside those blocks, I would be reluctant to avoid navy as it will look like the navy parts of the quilt aren't quilted. The same would be true to a lesser degree if you pick an exact match to the tan. I try to pick something that will show up equally on all parts of the quilt top -- either by using thread that matches my background fabric(s) or by picking thread that contrasts with all my background fabrics. With a custom pattern, the former is achievable by switching thread color so that it matches each fabric. With an all-over design (pantograph), typically the only option is to pick a contrasting color or tone.