Generally speaking, the less you handle a tree frog, the better off it will be. You can handle occasionally to medicate, inspect, etc. Remember they are very fragile and stress quite readily.
You can try mealworms, it may not eat them. Disregard the rumors about mealworms boring through the stomach of tree frogs, for this is not as common as suggested. You should try crickets as soon as feasible, they are the most common tree frog food. Dust lightly with a vitamin powder once or twice per week.
Skittish? not sure what this means. They are nocturnal and are quite aware of you if you are "observing" them. They will most likely view you as a predator, and will therefore not be very active if they are aware you are there. I have had greens that really couldn't care less about being observed and were very active. This is really dependent upon the individual frog.
The bigger the tank the better. Remember these are tree frogs, so the taller the better. You will hear 10 gallons per frog, etc. That is the guideline for survival. Provide the largest enclosure you can, again, taller is better for arboreal species.
bedding can vary. Forest floor mix is good for frogs and plants. In a small enclosure you will have to clean often, so a paper towel substrate is common. Again, provide a close resemblence to the native habitat if possible. If this is not possible, provide an environment conducive to cleanliness.
Basking lamps are not necessary. Provide the standard light dark cycle and if you can, gradiate the temperature and allow the frog to choose a temperature zone. You may use standard aquarium bulbs. Light is more for the plants, than the tree frog. Ambient light can suffice, just steer clear of windows, for they will raise the heat quite easily.
Furniture should be of the arboreal nature. Branches, golden pothos, philodendron are quite common. A water feature so the frog can soak if necessary. Humidity between 50-70% is adequate, too high or too low for prolonged periods will promote stress, illness, etc. Be aware of fertilizer in plants, for frogs absorb moisture through their skin, and fertilizer can be lethal. If you buy a plant from the store, ask. If they don't know, soak the plant in the sink for a while and rinse thoroughly to help the fertilizer leech out.
temperature around 72-80 fahrenheit. 70's during the night, slighltly warmer during the day.
good luck to you and your new friend!
-brian