IMHO, I would go with a natural fiber like cotton. Nylon will brake down very quickly in the sun light.
On the other hand, cotton brakes down when constantly wet (and stretches), but I've had the same cotton bow line on my boat since '97 and if the boat's not in the water (it almost never is) then the rope is laying on the ground in the mud.
Just buy a roll of twine. For one thing you get a lot for super cheap. You could have something more permanent that costs more, but it would be a pain when harvesting time comes. I don't imagine you have a cherry picker or something. You'd have to stand up there with your ladder or whatever and pick the vine for a while. If using twine you just cut it and the hop vine where it meets the ground and top support, take the whole piece, then sit on the ground with a bucket and tarp laid out picking away. Much more comfortable that way than being up high for a long time. Something more permanent would require unraveling the vine from it, then taking it down and harvesting unless you have some way of staying up there.
I was actually thinking about hooking set of permanent ropes up to SS disconnects (caribiners or something). See, I think I am going to run a SS eyebolt into the side of my garage at the ridge and string 6 ropes out to stakes, like a 1/2 xmas tree.