Beagles are hound dogs with a strong prey drive as they are originally hunting dogs. I would avoid any dog that has specifically
hunting purposes in its breeding history - hounds, springers, pointers, shepherds, most terriers and even some retrievers. That sounds like it doesn't leave much but if you wanted a rescue you wouldn't be sure what you would get, anyway. I highly recommend rescuing dogs, of course, or any animal, but for a first-time dog owner against what a lot of people recommend I would go for a purebred or single cross breed. You just know so much more what you are getting with a dog breed than a cat breed - they do tend to exhibit highly the characteristics they are bred for.
I can't recommend poodles highly enough - standard poodles, that is. Miniatures and toys especially can be more high-strung but standard poodles are athletic, gentle, highly intelligent, laid back sweet dogs and perfect with cats. Having said that I had two German Shepherds who were amazingly beautiful with our cats but that is NOT a breed I would recommend to the inexperienced owner they are incredibly high maintenance with a long puppyhood, and very powerful, strong dogs.
I would strongly recomment against anything with terrier in it - they can be sweet dogs but are strong willed and stubborn and Jack Russells in particular can be snappy and are NOT good with cats.
You could go a poodle, a labrador - that would be my number one pick - although they are retrievers they are lovely, lovely dogs, or some sort of labrador cross, labradoodle (I have two of those - heaven), cocker spaniel (although once again a hunting breed smaller and easier to handle, though not overly bright
), a Schipperke (gorgeous) or any of the medium sized more low-maintenance breeds. I would avoid at all costs working dogs, like blue heelers or border collies - once again a high prey and herding drive and not good around cats.
There's lots and lots of choices - here's a really awesome and informative link for you on dog breeds.http://www.dogbreedinfo.com/abc.htm
Good luck!! A dog will bring joy to your life like you have not known, I promise, and they are wonderful, loving, loyal, sweet friends and companions, and are my whole life (with my kitties of course!)