Hmm, a sweet autumn clematis sounds good. Have you thought about a conventional clematis?
For an annual, I would suggest a scarlet runner bean or a purple bean hyacinth vine.
Lately I've seen what looks like the love child of a honeysuckle vine and a forsythia. I don't know what it is but it's in bloom right now.

I had to laugh at "not very large".
Have you any experience with vines? Like mold, weeds, fungus, etc., they all start small.

I'd have to agree with a clematis, but a sweet autumn clematis is also known as a "castle killer" because it gets so big it can pull down walls. Like wisteria, ivy, vinca, chcolate vine, honeysuckles (both local and Chinese) etc.

Something like a named variety, Jackmanii, or such can be nice. They're perennials, too.

If you're (crazy) still looking, I have the last 3 I mentioned, including 3 Chinese varieties. Beautiful, but agressive.

Thank you for your ideas. I guess I should have been more specific about "not very large". What I mean is, something that is flat against the fence, therefore requiring a very little to no mulch bed.