Hmm, don't know about breed compromises. Would it do any harm to suggest to your parents the breed you want, since you'd be doing most of the training?
Seven years ago, when I got my pup, I took an online test that examined my lifestyle, and matched me with a good breed for me (I wish I could find it and link it now). It matched me with a German Spitz (American Eskimo), and I happened to find one in foster care in a city nearby where I lived at the time (Portland, Oregon actually). My aunt had a toy sized Eskimo when I was growing up, so I was already partial to them. My Soapy is a miniature Eskimo, which is the next size up.
Eskimos can be pretty nervous, and they are affectionate and loyal to a fault. I have never known a dog to NEED cuddles as much as her. I got her at nine months old, and she had potty training issues for another year. She also has developed anxiety over certain noises, which is a complete mystery to me. The sound of text notifications on phones (of ANY type) makes her tremble! Overall though, save for a shrill little dog bark, she is perfect for me. She knows tons of tricks now, and is the absolute light of my life. I originally wanted a full sized Spitz (which are still medium sized), but I don't regret having one her size. I take her everywhere I possibly can.
I saw all the great pictures of you and your fire cats. You will of course share pictures of the new pup when you get it, right?