I don't think it'll matter whether it's vertical or lateral. Sweet Autumn seems to grow in ALL directions! I'd make it something strong enough though, because 3 SAC's are going to grow A LOT! You'll have more problem with keeping them in their place lol!
I just planted my first terniflora SAC this year (about 1 1/2 months ago) and it's already doubled in size.
The first one I got in the mail order was the wrong kind. It wouldn't grow much at all, so I bought another from a different place (Joy Creek) and it's been growing excellently!
Like I said, it won't matter vertical or horizontal but stand back and let 'er rip! Next year they'll be eating your lawn furniture lol.

Cathy

If it is a solid wood fence it will need something narrow like a wire livestock fence panel to grip.

SAC will grow twenty feet or more.

You might want to look at the very end of a recent thread where there are pictures of wire fencing.

HereÂs a link that might be useful: clematis on a fence?