mutts are my preference. I had a cocker/retriever mix for 22 years. She was the perfect family member.

I am not into poodles, but poodle crosses seem to be good in the non shedding department. I have a groodle here every 2nd week, 13 years old and never sheds. Short hair is no guarantee, my dane/shepherd cross has short hair, and it is everywhere.
Older dogs are great and need homes too, less need for runs.
I saw other comments and I agree, an animal from a shelter, have a look at some and choose the one that fits best with you. Bit like dating.

I would recommend you go to a rescue shelter and look around. It is like going on the first date. Unless you fall in love with a dog, you don’t make a hasty decision. It may take a few trips before you find a dog you will fall in love forever. Good luck to you.

Don't get a Siberian Husky, their beautiful with blue eyes, don't bark, like to play and are the dog's world greatest escape artists.

Greyhound excellent choice. Of course be sure it's a cat savvy one! Shame your ex didn't like dogs. THAT is a HUGE deal breaker to me!