If you've had a dog before with your cats, it would seem they would adjust to another dog. It does take time, and some animals never do get along. Every situation and every animal is different.
We have 2 dogs, a lab mix (90 lbs) and a maltipoo (10 lbs). The maltipoo was here first and I was worried about bringing the bigger dog in. Guess who rules? lol. They are hilarious together and I know would be lost without each other, but the first few days we were extremely watchful over them. So, my best advice is to not expect an immediate "glad you are here" reaction, but don't let that deter you right away. Give it time. Unless your heart is set on a puppy, you may want to contact some rescue organizations or your local humane society. You may be able "try it before you buy it" with some agencies. Sometimes they even have puppies.
Good luck with your decision. Animals definitely fill our lives with lots of love.