Natural foliage is great, just double-check for toxicity if other than branches and vines.
One draw-back with natural foliage: they can die or rot.
They can house mites and other unwanted visitors.
They cannot be cleaned, as in disinfected/sterilized like fake plants.
If one breaks/dies/etc. it is not as easy to replace with an identical one.
However, they do offer the best visual look, and if done right, can last a long time. They are however, more adapt for out-door enclosures.
Fake plants are more expensive, but they can be more easily cleaned/disinfected, they don't "die", and can be easily kept outdoors/indoors. One problem is, they may not be always sturdy to withstand the abuse of claws and weight of the animal.
Real or fake foliage should always be inspected for spiders/mites, etc. Also, some people soak either in a bath-tub in a water/bleach solution, and then rinse thoroughly. The same done with rocks taken from the land.
Sounds complicated, it really isn't.
Make sure brances can be secured with nails or screws. Gorilla glue is a tough non-toxic glue that bonds things very well.
Rocks and branches can be cleaned using steamers. Actual plants, if real, cannot, so think about it.
Make sure that whatever natural plant you acquire, it won't become food, and if the iguana eats some, it won't be toxic.
Can't wait to see pictures once finished!
-IJ