I guess another point about tunes like Greensleeves or Twinkle Twinkle is that you already know them- they are so common that almost anyone could hum them from memory. They might be utterly banal but their familiarity gives you a great starting point when you try to get under the hood and see how they work. There are lots of other choices you could make- but what you want is simplicity and familiarity. These sort of tunes are also really helpful for when you want to move up a step and learn to sing and play guitar at the same time.
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