I haven’t woven a lot of placemats, but have done a few using cotton rags. The colours used were based on pieces of scrap fabric given me in colours of the final recipients choice and I bought more to make it go the distance.
I used a warp of mixed cottolin colours randomly sleyed (sett at 18 eip)and wove about an inch and half with cottolin for hems. The cottolin hem shrank a little too much, even with the use of a temple stretcher to make sure it was the same width as the rag section. But can be pressed out again (if you like ironing!)
The rags are all cotton cut into fairly fine strips of approx. 1/2 -3/4 inch depending on the type of fabric. I tryed to make sure they were about the same thickness when woven. The degree they compress is dependent on the hand of the original fabric – a finer cotton will be a small diameter, so I cut that fabric thicker.
I cut all the fabric before hand, laying them out beside me on a bench so I could chose them as I wove. I wove them in random order, trying to alternate the lights and darks and trying not to weave the same order over and over.
These mats are now about 10 years old, well used and going strong.