To make my yard more private, I want to mount a trellis or livestock panel on top of a fence, then grow climbing vines such as Distictus over them. Should I attempt to train the canes to reach 2M up without side growth, or would it be better to hang containers on the fence so growth can proceed directly onto the trellis? (If the latter, please provide clues what size containers would be appropriate.)
It's always best to plant any vigorous vines like Distictus in the ground - putting them in pots or containers will restrict their growth, and that's not an effect you want in these circumstances. Distictus buccinatoria reaches up to 4.5 metres, and will cling by itself to brick or stone; on wood, it might or might not cling, or it might need support. Ultimate height and spread at maturity around 10 x 25 metres, and there should be no need to train it as a single stem initially. Other vines may need different treatment.
The only other thing that occurs to me is, a trellis or livestock panel mounted 2 metres above ground, when covered in growth, is vulnerable to wind damage - if you want privacy in that area, have you considered planting a row of small to medium sized trees instead, if the area is suitable? That would certainly give cover 2m above ground, and more quickly.
Either build a support structure, or let it do it's thing. Do NOT build a temporary support for it. The main stalks can grow to 3" or greater in diameter when supported from the ground, and you'll want it self-trained to cling if that's the eventual goal. Otherwise, it will end up leveraging on the fence-top trellis.
Hellvine (which is what Trumpet Creeper is called by anyone who has tried to eradicate it) is a great plant-and-forget vine. It has a lot of adaptability built-in to its genes, it's hardy, and invasive (on a native level).
My recommendation is plant it, and every month or so, inspect it to see if there are any shoots you can cut off and stick in the ground in new locations to fill out the coverage. It'll learn to cling eventually - it's very self-competitive.