What is your experience with bringing a new pet into the home?

We are thinking of getting a dog for companionship. Last week, with the 4th of July, we had a neighbor's dog (didn't know that then) show up on the porch. She had escaped frightened by the noise from the neighbor's yard. They had gone out of town for the weekend, which we assumed so kept the dog overnight until we heard from the owner which I contacted from information on the dog's tag. The following week, the dog returned bright and early one morning, this time was frightened because of a thunderstorm in the area.

My mom doesn't remember much, but did remember the dog, one week later which completely astounded me. She must have made quite an impression on mom because she asked me if it was the same dog that was here before. She loved having the dog even for one day and actually remembered her a week later.

You read so much about what good therapy a pet is for people with many sorts of disorders. I would like to know of your experiences with bringing a new pet into the home.