I have never had a frog (or toad) bite my finger.
Perhaps some type of tree frog? Perhaps best for you would be the White's Tree Frog. Also the Oriental Firebellied Toad is recommended.
Crickets and beetles are better than just worms. And they need some frog vitamin supplements, like ReptoCal.
I'm interested in raising my first pet frog. What species of frogs require the least amount of special maintenance? Frogs that enjoy room temperature, do not bite fingers, eat worms (I'm guessing I could buy a large amount of worms at the pet shop for a low price). Also, I would prefer a non-aquatic frog, because if I wanted to fill a fish tank with water for a pet, then I would just get fish.