I don't have any recommendations as I am rather clueless on the vine topic. I'm growing a Wisteria vine in a 50+ gallon pot and it seems to be doing well. By doing well, it's flowering and sprouting everyday. What I don't like about Wisteria on the balcony is that its leaves droop here and there. Mainly because of the wind and receiving only AM sun.

For the hardiness of clematis, it depends on just which clematis you choose. Since you are in zone 6, you should choose something that will make it in zone 4 (potted plants are less cold hardy than those in ground).
Comtesse De Bouchaud: USDA Zone 3a
Sweet Autumn: USDA Zone 4a
Warszawska Nike: 4a
Ville de Lyon: 4a
and many more.

I've grown one in a self-watering pot that is around 20 litres = 5 US gallons. I added some pine bark mulch to the soil, to slow compaction.
You probably wont be able to fill a trellis in the first season, but you could sow a bean or two next to it to help fill out that trellis. Being a legume, the bean also adds nitrogen to the soil, so that might help your clematis grow a bit faster.

Ivy can be slow growing. Clematis is a good idea-- some are even evergreen if that is a desired trait. A climbing rose like Felicite et Perpetue is also evergreen and the whole foliage smells strongly of roses. I have hardy star jasmine which is doing well in a shadier spot. If you wanted to go annual, morning glories or cobaea are nice ideas.

Speaking of roses. I'm now growing (for the second time) a rose called Zéphirine Drouhin (aka Charles Bonnet). If you want a climbing rose, this one is highly recomendable. Blooms repeatedly with very scented semi-double pink flowers. I have read somewhere that they will be alright in more shaded areas, but I don't know if this is actually true.
The red canes are quite thin, and easy to bend, so that you can attach it to a trellis. It's virtually thornless, which makes it ideal on a balcony, where thorns otherwise can be quite a nuisance. I have to say though, that some plants (like the last one I had) might get tiny little thorns with a foot or so between them, but they are so small and few, that this isn't much of an issue.
I grow mine in a self-watering pot, that contains about 4 gallons (15 liters) soil. Again, I have mixed pine bark into this. This will over some years turn into soil, and make sure, I don't have to change all the soil for some years.
In the winter wrap the pot in a few layers of bubble wrap, move it to the wall, tug the canes down behind the pot and give it loads of mulch (as much as you can top up on the pot).

VG

when it comes to outdoor space. Pennsylvania bluestone is a great way to do it once and ad equity to your home. And outdoor kitchens are all the rave Bluestone Is a good choice for stone because it is quarried right in the United state and it is great for sustainability too.

I'm on a west-facing balcony with multiple pots of climbers to make a shield. I use several to get different effects during the day/year. I have morning glories and moon flowers (one starts blooming as the other stops during the day). I have winter jasmine and star jasmine, which bloom at different times of year (winter/spring, summer/fall), and I have bougainvilleas to add more color. Morning glories and moon flowers grow FAST (sometimes too fast), but I'm not sure how they'd do on an east facing porch.