What's the difference between "пойди", "иди" and "начни идти"?
"Иди" is imperfective, while "пойди" and "начни идти" are perfective. However, as far as I know, both "иди" and "начни идти" are used in the sense of "Start going!" or "Start walking!".
It's interesting that if we turn "пойди" and "начни идти" into infinitives, then they will both mean the same thing: "пойти" = "начать идти". However, the imperative forms seem to show some difference in their usage.
For one, is that "пойди" is, according to my observation, never used in the sense of "Start walking!" - the form "пошёл" is used in such case instead ("Пошёл!").
Another difference that I can sense here is that "пойди" always requires some additional modifier. Usually it's a modifier that adds some info about the purpose for the action of going/walking: "Пойди к Сергею.", "Пойди за молоком.", "Пойди на концерт."
"Начни идти", however, doesn't need any such modifier and sounds complete as it is.
Are there any other nuances that I don't see?
EDIT: Please, note that I am not asking about "сходи" or any other words! I am only asking about the words that I mentioned in my question.