Over the years, we've had two pairs of cats. All four were adult shelter cats. Our first two, Annabelle and Elizabeth, picked us out. I put my hand by Annabelle's cage (I couldn't see inside) and a little black and butterscotch paw reached out and curled around my finger. My husband noticed a dilute tortie who was intently watching every move we made. That was Elizabeth. The two in the photo are Mehitabel (black) and Martha (tortie). Both of them kept following us around the cat room. When we picked them up they both relaxed and closed their eyes. Martha even gave us kisses.
My husband firmly believes you go into a shelter with no set expectations and wait for a cat to pick you. Based on our experiences, I believe he's right.
Arlington Heights, IL