What machines and equipment do I need to start a clean paper and nylon recycling business?

There are many, many articles on the challenges of recycling specific single materials, like nylon or clean paper. Here's one for nylon. Talk to enterprises that are doing the same type of work in other geographies. Visit them. Maybe even volunteer to work there for a short period to learn more about how things work. At least tour the facilities.

Clean paper is much easier, as it is often tied to other related businesses like shredding confidential documents that are more profitable than recycling.

One of the biggest challenges in recycling is finding people who want to buy the recycled materials. There are too few of those. If you can figure out a business that buys and uses recycled raw materials, that's probably a better idea, because it will incentivize the people doing the recycling to do more of it, and they already have the costly infrastructure.