If you want to get into showing and breeding, why not start with this girl. Believe me, you will learn a LOT. But the showing HAS to come before the breeding. You need an honest unbiased evaluation of what your girl brings to the table. That will give you a basis to pick a male that will accentuate her good points and compensate for flaws.
That will also give you a chance to learn more about the dogs in her pedigree. You know that many are champions, look up their records on akc.org. Find out what they produced when they were bred. What lines make for the best combo?
As I said beofre, please don't breed "just pets". Breed the best saints that you can. Healthy, active, fitting the standard. Try to breed the perfect dog. As the saying goes, "better to shoot for the stars and miss than aim for the gutter and hit"
Everyone litter is going to have a range of dogs from show quality to minor flaws. But what happens when someone takes the pup with the minor flaws and breeds it? Then you are going to have more minor things show up. The same for the next generation and the next. Finally, you end up with a dog that is only a dim imitation of what it should be
ETA: no matter what else you do, at an absolute minimum you need to learn what all those titles in your dog' pedigree mean. Then go forward with the health-testing. Then add all that info together to decide if she is really a good brreding cantidate. Even if you don't know of any local breeders, there might be a reason for that.
Until I started researching, I. Didn't think there were any GSD breeders in the area except the ones who listed in the local classifieds and were not the type of breeder I would ever support. Turns out there are a dozen within a reasonable driving distance. Why does no one see those dogs? Because they rarely sell locally, instead having presold their litters long before the breeding takes place. Some have waiting lists over a year in advance.
Those are the contacts you need to make. Contact the st. Bernard club of america. Become a member. Meet other breeders and get involved at shows. Then compare your dog with what you see. Find things in their dogs you would like to improve. Make a clearly defined goal for your breeding program - you want dogs that are A, B, C and D and then pick a stud that will sire pups to bring you closer to that goal. Every generation should bring you closer to that ideal. Any pups not making the cut sold to pet homes where you know they will live a long and healthy life because you gave them the best start in life.