Only humans are allowed in my house.

Cats....unless it's trained to stay off tables, counters, anywhere there is food.

A wildebeest, as l live in a small place.

I don't want anything I have to clean up after that does not make it worth it to me. Now having said that I cannot think of some critter that would fit.

Birds. They're noisy, difficult to socialise, and smell weird.

Ferrets are definitely above my pay grade, so are rabbits. My girl has been BEGGING me for a rabbit for YEARS. We wouldn't be a good home for either so that's out the window.
Having lived most of my life with cats, and while I do like cats, except ferals, am totally in dog mode the rest of my years.

Hamsters, mean little assholes. I really like guinea pigs and even rats are smarter and nicer. I had a bat for a pet, also dumb and ill tempered and hard to maintain. It was just a novelty, I would never have another.

As long as it's in a secure box, cage, container then anything can stop by. If I'm expected to cuddle a tarantula forget it

I had a ferret for a while it was obnoxious and mean and it smelled really bad I sold it to my nephew

Skunks also.

I will take in anything, except humans. I'm not a huge fan of ferrets or birds (but I have had birds before) but I will take them in if they need a home or are injured.

If it can't purr like a cat... I don't think I'd want ti.