Oh boy, will you get a lot of answers!
What's right will be different for each dog and owner. It has to be right for both. The right equipment in the wrong hands is just as detrimental to the dog as the wrong equipment for the dog.
That being said, puppies usually have a soft collar and a soft, 1/2" wide lead. Coax, but do not pull the puppy. Reward.
For Myah, we went to a soft martingale and wider soft leash around 4 months. She had that for a while.
Then we went to a soft martingale with a chain section (same leash) around 6-7 months. It rusted at the beach and didn't release well. So, I got a bigger (1" wide) soft martingale.
Then about 8 months, she had a Herm Springer prong (which she only mildly needed, and not anymore, but she's used to it) and a 3/4" fake leather European adjustable leash (I wear it over my shoulder - love it! - fake leather goes to the beach well). But I also have a Dean & Taylor canvas harness.
She's collar-less in the house and yard - always has been.
She also does pretty well with off-leash work.