The colors you have on hand are perfect for piecing. I use CT’s “Natural” almost exclusively for piecing. I do have a collection of colors, but I use them for quilting, not piecing. Whether you machine or hand quilt, you may want colors besides these for quilting, but some people only quilt with white or off-white, so it’s just personal preference.
You didn’t ask about brands, but I use CT for everything. I have dabbled with other brands, mostly Superior, but I don’t find I get proportional value for the very large difference in price. Other users have different opinions; you will have to decide what works for you.