-かける versus －だす versus －はじめる

[dshadoff]

Could somebody explain the difference between the post-fix verbs -かける, ーだす, and ーはじめる ?

For example, take 話す:
話しかける
話し出す
話し始める

What are the subtle differences in meaning ?

It seems to me that：
話し出す would be a more direct and unrestrained way of "to start talking" (as in somebody blurting something out
話し始める focuses on the act of starting, rather than the action being started, and
話しかける sounds like a more gentle, restrained or gradual way of starting to talk (as if to a stranger).

Is this correct ?