Hi and welcome to the forum! To start with, don't you have a way to make your arbor a little taller than 6 ft high? If it is to shade your patio, I take it people are meant to be walking under it. Lots of people are more than 6 ft tall. I am not, but even so a 6 ft "roof" is a little claustrophobic. 8 ft would be a much better height.
So evergreen vines:
Personally I would go with jasmine. There are several different evergreen jasmines, star jasmine, pink jasmine, Carolina jasmine (which is not a true jasmine). They have a heavenly fragrance! They are quick growing and will eventually cover your area well, without getting too huge and heavy or taking over the yard.
But there's several other choices: evergreen clematis, morning glory (watch out!, invasive), cape honeysuckle, creeping fig, pink bower vine, passion flower, crossvine, evergreen honeysuckle vine,
How big should "the" container be to cover the space? If you want the space covered any time this decade, it is not "the" container. You want a large container by each support post. You could even do different vines in different containers. Here is clematis and jasmine growing together:
(though to be perfectly honest, the purple clematis is not the evergreen one. Evergreen clematis has smaller white flowers.)
But tons of possible combinations. Here's passion flower and jasmine growing together: