A lot boils down to personal preference.
I prefer cotton, so that is what I buy. I prefer to match fiber with fiber - I quilt cotton cloth, so I use cotton thread.
In one class I took, we worked with polyester threads. While the claim is that they are smooth, I can feel roughness on that very fine thread (prewound bobbins). It was not a case of slubs like you can find on poor quality thread - but like little barbs along the thread. Probably did not help that I had very dry fingers at the time.
Harriet Hargrave is emphatic about using cotton.
The polyester thread makers are equally emphatic about polyester.
Do avoid threads marketed for sergers as those are not intended to be as strong as 4 or 5 threads are used together. Rayon for embroider won't hold up as well either.
My favorite for piecing is 60/3 by Presencia. It is a very fine/very strong thread.
Cheers, K