From your title, I assume you want best variety of trellis, rather than variety of blackberry. This much-discussed topic can be found by searching this forum for "trellis". The best type of trellis may depend on the variety of blackberries being grown.

I hope people comment on this since I think it requires a somewhat different/simple trellis.

I'm not into trellis because I have to keep the canes growing as low as possible for the ease of winter coverings...come spring then the I tie the surviving canes up from the ground..nothing special required. One thing you have to keep in mind when growing canes on trellis is that every year you'll have to cut the finished producing canes out...so make the trellis and hanging system as simple as possible.

Ok...didn't get it first, what's the best cultivar on trellis...at least you want a thornless for the ease of removing canes.

I am in southern zone 8b near 9a and am currently growing 4 varieties of thornless blackberries Prime-Ark Traveler, Osage, Ouachita, and Sweetie Pie. (4-10 plants of each). Out of these the ones that seem to be easiest to manage on a trellis are the Prime-Ark Travelers and the Ouachita's they seem to grow fewer longer canes, where the Osage and the Sweetie Pie's seem to grow many bushier shorter canes in all directions.