Update: I found the book with the help of my local library, it's called "Pets for Sale" by Rita GelmanI remember reading this book when I was a kid. I read it in the mid 90s. A little boy is looking for a pet, and visits this very odd pet shop; I remember that the entire story was in rhyme.(It wasn't Puck's peculiar Pet Shop by Dean Walley and Roz Schanzer, although it was somewhat similar to that one.)The pet shop owner presents him with several different pets, each with some bizarre and annoying trait, such as a robot-like creature who cleans up everything and a minotaur-like creature who messes up everything, a creature with a scissors-shaped head and(I think) a glue-brush shaped tail who cuts and glues whatever he can get his hands on, several tiny, car shaped creatures who go zooming everywhere, a raccoon in(I think) a Centurion helmet who causes various kinds of mischief, and a giant sphinx-like creature with a TV-screen face who breathes fire. The boy(as one might suppose) turns each one of them down, until he's presented with a regular, normal dog. (spoilers for the end of the book) The pet shop owner insists that the boy couldn't possibly want the dog("She does not cut, she does not glue, she is not the pet for you!), but the boy knows better("Says who?) then they leave together.
A pet store owner has many strange animals to pick from, but the pet a young boy finally decides on is a big surprise.