Wrestling Game

I have been teaching myself UE4. I want to make a small demo of a wrestling game. My question is would I do the ring ropes as a animation or would I want to do physics or a combination of the two?

If you’re just learning UE4, I’d suggest you to make the ring ropes to be just a static mesh with no interaction.
Implement the basic gameplay, fighting etc, then update the ropes.

As for the question itself: here is a tutorial about how to make a physics based ropes.
Other option is to use beam particles to simulate the ropes. It all depends on your requirements and skills.