I used Red Heart Super Saver yarn for the dark brown and black, and Caron Simply Soft yarn for all the other colors. This was because these were the only brands I already owned for the colors I wanted... if you actually want to create your own latch-hook pieces, you ideally shouldn't use either. Red Heart Super Saver is very stiff and on the rough side (for a pillow, anyway) while Caron Simply Soft is fairly thin for the latch hook canvas size and unravels easily.
In terms of both softness of texture and possibly yarn weight, I would recommend trying Red Heart Soft or Lion Brand Vanna's Choice yarn (though no guarantees because I actually haven't tried these myself.) Caron also makes a "craft & rug yarn" that might be good for this - they sell their own DIY latch-hook kits and this could be the yarn they use for those.