Schutzhund is NOT equal to careless attack training.
It is highly disciplined, very much controlled, and only dogs of a certain temperament are allowed. The average spooky rottweiler or GSD is NOT allowed in the protection work- only dogs of sound temperament, clear mind, and solid nerve are able to train in the work. These are typically dogs either safe in public and approachable or, if serious protection trained, owned by owners who take the dogs seriously and make profound life changes to live with a security dog. Schutzhund is not for the drug dealer, the white trash, nor the people that think a snarling, biting dog is cool. Schutzhund trained dogs are amongst the most well controlled, highly trained, safe dogs out in the world! Done as a breed test, it helps choose the future of the GSD.
A GSD can be obedient if it is trained properly. Be aware that the GSD is very smart, very intelligent, a quick learner, and a good thinker. If you have experience and knowledge, the GSD is very easy to train. I can teach my mix (which has mostly GSD characteristics) new things very, very fast and he retains the knowledge quite well. However, this is a double-edged sword. If you're not experienced, don't take your dog to regular training classes, and don't work its mind on a daily basis, you are going to suffer! Imagine a very smart, creative kid left to his own devices by himself in a house with no rules. Chaos, huh? Well give that kid a mouthful of teeth and it gets even worse.
Most GSDs are anything but mellow until their later years or unless they come from breeders specifically breeding mellow dogs. Intentionally breeding mellow GSDs is completely against what the GSD should be, though! IMO, it's deplorable. Might as well breed 22" high chihuahuas, labs that hate water, greyhounds that can't run, cattle dogs that have no instinct to herd, and border collies that are lazy. GSDs should not be bred to be pillows on the couch! Having said that, I'm sure you want a mellow dog that's relaxed after plenty of exercise, say a couple good walks a day or a solid game of fetch and a few minutes of training. This is perfectly fine and lots of GSDs will fit this mold. Most working lines may be too much unless you're willing to provide for their mental and physical exercise needs, then they can be fantastic companions. Otherwise, either of the showlines would fit you but you'll find strong preferences amongst the types. Mine is to the working line, this is the original GSD type.
You will find that a lot of owners with GSDs may not do much with their dogs but they do have issues here and there. These are not the best dogs to have as "just a companion" unless they give them plenty of exercise, stimulation, leadership, and training. They're not like some breeds where you can do minimal socialization, just "sit stay down come" training, and walk a few times a week and have a good dog that will love everyone. They do take a lot of work and I do not feel that German shepherds are right for everyone nor should they be. There are plenty of other breeds that have the nobility that have better chances at being mellow, friendly, and more sociable. Most GSDs will not mature into social butterflies and some couldn't care less about playing with other dogs. They should be politely aloof, but as puppies they need extensive, major socialization. Think carefully and ask yourself if maybe another breed may be a better match. If you wanted the very large size, nobility, and mellowness, I'd suggest the shiloh shepherd but I hear they are having temperament issues.