For my balcony space I decided to go with two different vines for each balcony divider, a honey suckle and a star jasmine. These small 8-12" vines from the local nursery were planted in 23" self-watering planters. The planters have a water resevoir below, the water weighs down the plant and makes it more wind resistant, perfect for a balcony. For the soil, Miracle Grow Moisture Control was used, the vines were not fertilized for the first 6 months.
Vines grow extremely quickly, especially in the spring to early summer months. Both of these plants are "full sun" plants, but seem to do well enough on my north facing balcony that only receives indirect light.
Most vines are generally hardy and require very little maintenance. Water regularly and never let the top soil run dry. Regular pruning is also recommended to get the vine to grow bushier. After the oscomote tablets run out in the starting soil, fertilize with oscomote tablets every 2 months, or water-soluable general fertilizer every 2 weeks during the growing season.
What if You Don't Have an Existing Structure (Lattice, Fence, Wall)?