I'm so sorry for your loss. I too have had to have my beautiful dog put down due to sickness. She was one of my best friends and the sweetest dog I could have hoped for. When we were at the vet's office, they were crying with me.
She was actually purchased for my daughter but soon became mine. She would wait for me to arrive from work and be the the first one out the door to welcome me. It is definitely true that a dog is man's. or in my case woman's, best friend. You are right in knowing that your many memories will comfort you and in knowing that your friend is not suffering. Take care!