About Great Pyrenees - most of this has been covered, but it should be re-emphasized:
Great Pyrenees are livestock guard dogs only.  They don't want to play with you.  They don't want to obey your commands.  They were bred (for hundreds of years) to be independent and to guard.  They make lousy pets, but great guards (against predators, not people).  They are intelligent, but they don't use that intelligence to figure out what you want - they don't care - they know their job, and it's not to be a pet to you.
You have to make sure you get purebred Great Pyrenees or a GP/Anatolian mix only.  If you mix other (non-LGD) breeds in there, they won't have the correct instincts.  Most other breeds are hunting dogs of one form or another, and have entirely different instincts.  And the hunting dog instincts seem to be dominant.  Don't go to a shelter and get a 'Great Pyrenees' stray or rescue, or you're likely to get a mix, and then you won't be happy (assuming you want an LGD).  Don't go to a breeder that doesn't have livestock and can't demonstrate that their dogs have the right instincts. 
Great Pyrenees are born with the right instincts.  They don't have to be trained.  You need to introduce them, correctly, to the animals they're to guard.  Anything else is fair game to them.  If you don't introduce an animal to them, expect it to get chased away or eaten.
Great Pyrenees tend to sleep all day, stay up all night (since that's when most predators are active), and bark, a lot, at predators.  They prefer barking to attacking, and if the barking works, they're happy.  They generally don't need to be tied or fenced in.  Walk your property with them, they'll get to know it's theirs.  If you have a really small yard, they might expand their territory beyond your borders, but that's instinct - they don't like the predators getting too close, in your yard or not.  There are many other breeds of dogs that tend to wander off, get lost, chase things until they catch them, but not GPs.  Great Pyrenees will chase things out of their territory, then come back to guard.