You can find lots of information about Vishnu at Wikipedia, including information about his avatars (incarnations), and each of the avatars in turn has its own page, like Matsya the Fish, Narasimha the Man-Lion, Rama, Krishna, and so on, along with Vishnu's female avatar, Mohini. You can also read about the branch of Hinduism devoted to Vishnu: Vaishnavism. Plus, you can get lots of ideas from looking at past Storybooks about Vishnu.
You can read about Shiva and about Shaivite Hinduism at Wikipedia. Shiva's special abode is Mount Kailasa in the Himalayas, a sacred mountain in many religions. Shiva's special weapon is the trident called Trishula and he is often worshiped in the form of a lingam. For Shiva the cosmic dancer, see this article about Shiva Nataraja, and you can read about the special hymn Ravana composed for Shiva here: Shiva Tandava Stotram. Here are some past Storybooks about Shiva.
Hanuman, the monkey god who was Rama's most devoted follower, is a character you will get to know well as you read the Ramayana. You can find out more about Hanuman at Wikipedia, and you can listen to devotional songs about Hanuman at YouTube. Hanuman continues to be revered throughout India even to this day; you can read more about that at the BBC in these articles about monkeys in India today and their connection to Hanuman. For more ideas, take a look at these past Storybooks about Hanuman.
MORE GODS AND GODDESSES
In addition to Storybooks focused on the gods listed above, here are some more Storybooks about gods and goddesses from past classes. You will see many different stories about many different gods, and Wikipedia is definitely the best place to do your research.
Gods: Agni, Brahma, Ganesha, Indra, Shesha, and Yama.
Goddesses: Devi, Durga, Ganga, Kali, Lakshmi, Parvati, and Saraswati.
Plus there are the apsaras (celestial nymphs) such as Menaka, Rambha, Tilottama, and Urvashi.
Also, don't forget about the vahanas (the divine vehicles of the gods), some of whom are famous in their own right, such as the eagle Garuda and the bull Nandi.
(image source: Brahma, Vishnu and Shiva
with Saraswati, Lakshmi and Paravati).