My guess is that you can sign a contract with most of the animals. So far we seen frog, monkey, snake, slug(looks like you can even sign with insects), salamanda and even dogs (I'm not sure if kakashi signed a contract or trained them) ....if theres some I missed out please do tell.
Well bottom line is I would like to see how cool the monkeys are or I would just sign a contract with the toads, they have cool accessories lol.
[P.S. Since people are asking if they could make up their own animal, the answer is yes. Knock yourself out!]
"R.I.P Toad With The Cool Goggles"