Timber!

I've purchased the wood that I'll use to build the frame of my vertical garden!

I went with Mahogany for its color and density and it also happens to be an easy wood to work with compared to some other hardwoods.  Now Mahogany does have its issues, there are many supplies that can't guarantee that their wood comes from a reputable dealer who uses sustainable harvesting practices.  However, since Mahogany is very popular in furniture making it is easy enough to ask if the lumber is Forest Stewart Council certified (http://www.fsc.org/) by doing this you can have the peace of mind that whatever you're building isn't made from a tree cut down in one of the few remaining old growth forests.

http://www.pbase.com/placesandseasons/image/33165379

Mahogany trees can be found in Central and South American rain-forests and can grow up to 150 feet tall.  Throughout history this type of wood has been prized for red color and since the age of exploration it been harvested for fine furniture making. Currently, the United States is the largest importer of Mahogany wood.

Other good options for making a vertical garden are Redwood, Teak (sustainably harvested teak is very hard to obtain though), Locust, or any sort of reclaimed wood from outdoor furniture that can withstand moisture.

More information on Mahogany can be found at:
http://www.rainforestrelief.org/What_to_Avoid_and_Alternatives/Rainforest_Wood/What_to_Avoid_What_to_Choose/By_Tree_Species/Tropical_Woods/M/Mahogany.html