It actually depends on the type of application your are intended to for using polymer fibers. "Denier" is the most important aspect and unique characteristic of fiber to be taken care of.
Polymers, with fiber-forming properties, usually have linear structures with groups that allow for strong inter-molecular attractive forces with no presence of bulky side groups. Structure determines properties so these polymers will have high mechanical strength as well as high melting points.
Fiber-forming polymers are usually flexible with a high degree of symmetry on macromolecular scale & the macromolecules will have high molecular masses specially if there are no inter-molecular hydrogen bonds or dipole-dipole interactions.
The macromolecules will have capacity to assume an extended configuration that can be an adequate requirement for ordered alignment which points to high degree of crystallization. When the polymeric molecules look like "parallel" zigzags , then there will be a high degree of orientation of these molecules and thus there will be a good tensile strength.
I shall give 2 examples: Nylon-6,6 is well-known as a fiber-forming polymer & most of what I said above applies to it.
Polypropylene (PP) is also fiber-forming but many chemists do not know that. The –CH3 group is considered as bulky for simple organic compounds but it is not bulky in giant PP macromolecules. Once there is isotactic PP, with high average molecular mass, then there will be many London forces that align & orient the structure to render it suitable for forming fibers.
Carpets "containing fibers, of course" can be made from polyamides & polyesters but the cheapest are the carpets that are made from PP.
Note: Many years age, one of my "late" British professors was a great specialist in this subject. I just summarized what I was taught by him using my own language. I hope that I did well!
polymers must satisfy the minimum requirements if it is to serve as a fibre. Those requirements are (Flexibility, Molecular Mass, Configuration, Crystallinity, and Orientation )