I have yet to see a physical fence that will contain an LGD. They are champion diggers and excellent climbers! We use the invisible fence for ours. Train the new puppy to it right away on the mild collar (which is the equivalent of shuffling your feet across carpet and touching a doorknob), then at about 5 or 6 months when the teenage wanderlust kicks in, switch to the stubborn dog collar set to max and set the correction zone at least 15' wide.
Aside from having a golden retriever for a family dog when I was a child, my first dog as an adult was a Kuvasz. LGDs are NOT like other dogs, so as long as you understand that, then you will be okay - and if you've never had a dog before, then you won't know the difference

LGDs are independent thinkers, which means they won't always listen to you. This can lead to frustration, until you realize that the reason for the disobedience was because there really was something more important going on! They are very sensitive to punishment and harsh corrections, so training with a shock collar is not advisable. (The fence is different - it's an invisible boundary that is fixed, not a random "zap" that they can't understand.) They also cannot be tethered on a line, except for short periods with supervision, as this can create an aggressive dog.
As for the rooster, if there's any chance at all that he might attack your new puppy, do your chicken chores and regular flock tours carrying him at first. You don't want the puppy to be afraid of - or worse, defensive/aggressive towards - your chickens.
The playful stage is the most challenging, and it can last a looooong time! Try to stop chasing before it starts (this is tricky with a first dog, since you will be learning to read his body language) by redirecting the puppy's focus. If chasing does happen, stop it immediately and say a deep and firm "NO" at the same time, then remove the puppy and try again another time. Reward calm behaviour with treats and/or praise, and these rewards can be at anytime... Dog laying in the yard just relaxing, toss a treat without saying a word.
Raising any dog to be good with chickens is a challenge, but with the GP you will get a dog that is also protective and nurturing. If you're up for the challenge, I say go for it, and your efforts will be well rewarded

I loved my first Kuvasz so much that we now have three of them! Oh: if you lose a bird or two, it's not the end of the world