It seems that a cat would be a bad match for Hermione as a pet. Cats are playful and very disruptive, from my experience. NOT a good pet for a studious person with their head always in the books.
Of course Crookshanks was integral to the plot and ended up not being a simple cat, so she had to pick him. But it seems such an unlikely choice for her to make, compared to a toad or an owl.