I think a mature dog, from the shelter, that is calm, could be a very good addition to any household. I vote against a puppy or kitten. They are high maintenance.
I have four dogs so I'm biased. One acts very much like a cat, which is a good combination! I also like cats very much although I don't have one right now. Can't imagine life with no dog or cat.
It seems unnecessarily cruel to deny one's self of a companion like that. If you get it from the shelter, worst case scenario, you give it back. You did not bring it into the world and abandon it. You can even tell them you are new to this and are taking it on a trial basis.