I'm sharing my own personal experience and caresheet about green tree skinks and skinks in general since puro imported skink caresheets ang meron dito as well as sa net..
General rule in housing small lizards; allot at least a minimum of 3 feet floor space per 8 inches of lizard excluding tail length (except if your housing iguanas and other long-tailed lizards)
BUT!! because i don't have enough floor space but i do have enough tank height, i incorporated a lot of branches, wooden structures and flat rock pieces for the tree skinks since they spend most of the day high up from the ground. I don't recommend putting hiding places or re-creating their natural environment especially if you want seeing your skinks all the time, since i've noticed they become quite nervous even at the slightest sound or movement and will just shy away in their hide all day.
Substrate is important. If you put bedding like coco peat, wood shavings, leaf litter or other loose & light substrate, you're skink is most likely to dig even if it is an arboreal species. A false bottom, newspaper, sand, gravel, cat litter or any fine pebble substrate mixed with crushed charcoal (to absorb too much moisture and and bad odors) is fine not to mention easy to clean and doesn't smell that much (especially if tamad ka maglinis like me na once every 2 weeks lang naglilinis.)
Make sure to secure your tank cover!! Green tree skinks are escape artists and great jumpers.
Majority of skinks don't drink straight from a water dish so it is advisable to mist one side of the tank daily, at the plants/decors or directly mist at the skink's body. Since nasa tropical country naman tayo, regular misting is not advisable to increase humidity unless your planning to let your skink drink water. You don't need to worry about temperature or humidity but you can leave a bowl of water with something to climb on kung malalim.
Light is very crucial! They bask themselves at the first sight of light. No need to use UV light or lighting during the night since they are asleep during this time and is likely to be disturbed (unless you're keeping your skinks in a room with no natural indirect sunlight.) UV lighting is best used during rainy days or stormy weather.
Food: mealworms, superworms, crickets, lats & dubias or any insect that doesn't fly around will do. You can dust it with calcium+D3 or other herp vitamins if you wish. Green tree skinks also eat a little amount of mashed banana.. Common ground skinks loves earthworms, millipedes and small snails. They also love eating spiders and caterpillars even the hairy, itchy ones. You can feed them small geckos so as to provide calcium in their diet Just make sure you remove uneaten food to avoid ants and mites
Trim their nails once a month, check for mites, remove uneaten shed skin and scales and regularly check the tank for unusual odors.
You can handle your skinks every once in a while but this is not advisable for green tree skinks since they wriggle a lot, claw a lot and bite given the opprtunity (though di ganun kasakit from my experience). This is to avoid stressing your pet.
Thanks! Enjoy your skinks!