I am not aware of any species native to the United States as the white striped tree frog. Green tree frogs have a tremendous amount of variability in their coloration, they can have bold white stripes or none at all.
I am a firm believer that gravel should never be a part of any reptile or amphibians enclosure. The gravel can and will cause impactions for any animal that can eat it. Moss can also cause impactions or entanglements. On top of that, gravel is incredibly difficult to clean and disinfect because of the high surface area and porosity. The best way to provide the clean water source for tree frogs is a simple bowl that can be removed on a daily basis, cleaned, and refilled. The best substrate for green tree frogs is coconut fiber.
Absolutely, positively, they will become stressed that handled. Amphibians in general should not be handled unless it is necessary. Consider them a terrestrial fish. Even if they are handled, the professional standard is to use latex gloves that are rinsed free of powder and left moist. Especially when it comes to green tree frogs, they are very difficult to hold onto without them jumping onto unclean (or amphibian inappropriate) surfaces. Amphibians are definitely not the pet of choice if you are looking for something to interact with.
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...the oldest task in human history: to live on a piece of land without spoiling it."
Aldo Leopold (1938)
"Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has tried to contact us."
Calvin and Hobbes (Scientific Progress Goes 'Boink', 1991)