等 + [event] + (以后 / 了),+ [subject] + 再 + [verb phrase]
等(到) + [event / time],+ [subject] + 就 + [verb phrase]
等 + an event sets a future point: "once", "when". The main clause follows, and 再 before its verb says the action is being held back until then – not now, later.
以后 or 了 often closes the 等 clause and changes nothing in the meaning. 等到 is a fuller form of 等.
再 is putting off: don't do it until then. 就 is readiness: as soon as that happens, it'll be done.
再 is an adverb: it goes after the subject of the main clause, right before the verb.
English "when" covers both past and future. For a future point you are waiting for, 等 is the natural word; 的时候 describes the moment itself rather than waiting for it.
For the plain order of two steps, "first this, then that", 先…再 is the frame.