I am still figuring out hubpages, and just realized I should have answered this long ago! Please forgive!
There is no "easiest" dog to breed and show. Some are easier to breed, for sure. Some of the toy breeds, for example, have a hard time delivering puppies and are routinely delivered by C-section and at great expense. Dozens of breeds have hereditary health defects that must be searched out and weighed against that particular breed's personal appeal. One example would be that most (but not all!) lines of Cavalier King Charles Spaniels carry the genes for heart defects that generally kill them by the age of eight or so. The giant breeds are riddled with hip dysplasia. Something like ninety percent or greater of Shetland Sheepdogs will have thyroid problems by the end of their life. Purebred dog breeding just for looks (the competition in the AKC show ring is FIERCE!!!) has come at great cost to some breeds. There are breeds such as the English Shepherd, that do not want AKC recognition for that reason. The American Border Collie Association voted in 2003 to revoke the registrations of any of their dogs who attained a conformation championship with the AKC, and no working registry in this country will honor an AKC bred Border Collie's pedigree.
Anyway, I digress. My short answer is, the "easiest" breed to breed and show is going to be the one you love enough to persevere with. And by "show" ... well ... do you mean conformation? Obedience? Agility? Tracking? Flyball? Earthdog? An AWFUL lot depends upon what kind of showing you want to do. The "beauty contest" of conformation frequently comes at the expense of the breed's original purpose and brains.
It is a lot to think about, and I suspect you only threw the question out to me as an encouragement, anyway!
Thank you so much, and have a wonderful day!