I personally do not recommend nylon thread because it can be very hard for a home machine to handle. It can stretch very badly and that throws tensions off.
Regarding cotton thread.... The general rule of thumb is to match the thread to the fabric used. So cotton thread for cotton fabric. What that really means is cotton thread for natural fibers. Polyester thread for synthetic fibers. There are mixtures for "all purpose" use but as usual "all purpose" means it doesn't do anything really well.
The reasoning is this.... natural fibers are by nature softer than synthetics. You don't want the thread to cut the fabric as might happen if you use straight polyester thread on cotton. Nor do you want the fabric to cut thread as might happen using cotton thread on synthetic fabrics. While it is true that cotton rots in the outdoors, polyester deteriorates. To me that's a wash. It's the mixture of textures that bothers me and why I encourage not using cotton thread on gear.