My very first pet that I ever had (excluding my sweet bettas that I had) was a Cairn Terrier dog named Scottie. Currently, he is 11 years old, and still very healthy!
My very first small furry animal/s were two male mice. One was named Wheat, and the other was named Speedy. Unfortunately, at that time, I was very young and didn't know that you couldn't put male mice together. Wheat being the less dominant one eventually died.
As I look back on those memories, I have both very fond and very sad memories.