Great start of a collection thread! And welcome to the forum (and Discord). 
I know this question wasn’t directed to me, but I personally always thought Entei was based on a lion; Raikou on a saber-toothed tiger; and Suicune on a wolf.
But if you want to know what Japanese mythological creatures all three are actually based on:
- Entei is based on Shisa, the “guardian lion dog”
- Suicune is based on Kirin, a deer-shaped dragon with ox’s tail, the most powerful creature in Japanese mythology (with phoenix and dragon being second and third place respectively)
- Raikou is based on Raijū, the “thunder animal/beast”, usually depictured with a body composed of lightning in the form of a white and blue wolf or dog, although it can represent with other forms (see the huge list of animals on the Wikipedia page).
So they’re basically just mythological beasts, or catdogs if you will.
Greetz,
Quuador