I made climbing vines out of steel wire and twine. Shouldn't be more than $5 for roll of each, makes as many as you'll need. I double the wire for stability.
Cut two lengths of wire( a little bit longer than the desired length of the branch), take a pair of pliers, line up the wires, and then start twisting them together. You don't have to do it very tightly, as the tighter you twist them, the more length you lose.
Once finished, take the twine, and secure it to one end of the twisted wire. While keeping tension one the twine, start to wrap it around the wire, pretty much coiling it like a slinky.
Wrap the whole length of wire, and secure it to the far end of the wire. If you prefer, you can go back down the wire again, to do a second layer of twine for thicker vines. My guy is still on the smaller side, so one layer was good for me.
Finished product: