One of the things I like about learning to play the tin whistle and Irish and Scottish music is that my constant need to memorize new tunes (and songs, as I like to sing) is giving me a real mental workout. My day job also requires me to remember large amounts of information, but memorizing tunes seems to work a different part of the brain. Research indicates that "mental exercise" can reverse the decline in brain function in old age, so the more the better!
I notice, though, that the method I use to learn a tune has changed since I took up the instrument last year. Previously I would play the tune through until I no longer required notation (I wasn't doing much ear learning at the time). Now, however, I find it much more effective to learn a measure or a phrase and then build on that, one piece at a time. This seems more effective both when learning from score or by ear for me.
I spoke to a fiddler who uses a third method. He learns the first note of each measure or phrase — the "outline" of the tune — and then fills in the rest.
I don't know if any one of these methods is "best," but it's interesting that there are different ways to do the same thing.