what are the species of the characters?

I think in one episode Fozzie says Scooter is a dog.

One episode, I recall Scooter drawing some connections between himself and hummingbirds, though don't recall if it was just a joke.

I think Scooter and Skeeter are more along the lines of humanoid Fraggles. Scooter(from The Muppet Show) is kinda like the proto-Fraggle. If Fraggles are animals in Fraggle Rock, then in Muppet Babies, Scooter and Skeeter could be the equivalent of anthropomorphic Fraggles, just like Fozzie's an anthropomorphic bear(I pretty sure he looks different than some of the other bears seen in the Muppets).

Gonzo is a Weirdo. Muppets from Space point to that he's an alien, but that's what I think Weirdos, in the Muppet universe, are. Strange, "not of this world" creatures.

Animal, I'd think, considering the strange creatures of the Muppet universe, I'd reckon he's the equivalent of a "Beast"(like in Beauty and the Beast, some hodgepodge creature that's parts of different ferocious mammals, like lion, gorilla, wolf, and so on). He's like, "Put a gorilla, bear, wolf, and lion in a blender, and after mixing them up good, when you pour it out, that's what Animal looks like!".

Leave it to someone to bring racism to the muppets.

I think it would be easier just to classify them as "Muppets," which are a unique species of puppet that can come in any size, any form, and any color.

They were just...muppets. I know that on Sesame Street, the non-animal ones (like Oscar the Grouch, Elmo, Cookie Monster) were "monsters."