Plastic coated wire on a reel is quite good, but I'm wondering why you need to do this at all - clematis is much better left to scramble upwards by itself, either by climbing over and up taller plants nearby, or clinging onto specially put up clematis mesh netting - this allows the petioles to wrap round its thinner supports, which won't happen with a trellis because the wood lathes are too broad/thick.

i encourage them to twine by tieing them to the support with soft twine.