I am greatly flattered you have asked me this question - I am terrribly biased but I've had cats too and can understand your question. My best answer would be (from experience) that I rescued a 9yr old female Collie Cross when I had 3 well-established territorial cats of ages ranging from 7-12yrs and the rescue girl, Jilly bonded with all 3 cats within days, as did the cats with her! A lovely miracle.
It is great that you are now considering a dog - would you consider a rescue? I only ask as I would definitely do it again, as it is so worthwhile and rewarding on both parts. Cats are great but as I discovered, the bond with a dog can be so, so much stronger. Please have a serious think about this option.
If you are going for a pup, make sure you know where it is coming from. I don't want to preach but puppymills abound and you should ensure you don't buy from cruell/illegal sources and unwittingly perpetuate puppy mills.. If you need to know more about why you must know the origin of your puppy, please read my post on my site, which is wholly factual and terribly upsetting.
As for the low down on good breeds, I suggest you visit fellow hubber Whitney05 who has several articles on how to choose the best dog breed for you.Big tip, not a Westie, as I have, they don't share your attention or affection - they want it all! Westies are gorgeous but my little Dougie wants me all to himself - my mistake, I should have got another dog at the same time as him, such as a Collie!
I once had a Cocker Spaniel called Lovejoy - he got on well with my 3 cats too and was around when I rescued the Collie Cross, Jilly.
Let me know how you get on, I'd be interested.