I'm old school (film era).
1) Started out with 50 prime and 28 prime,
2) Added a 135 prime a few months later,
3) Followed by a 20mm prime a few months later,
4) Followed by a 300 prime another few months later.
5) After a long while more added a 14mm prime.
The advantage of this route is you get to know your focal lengths and their perspectives intimately. Disadvantage - frigging ex and lots of things to carry + not as flexible as zooms (debatable of course).
Subsequently when I started doing assignments it was the trinity zooms (mid zoom first, followed by telezoom then the ultra wide angle zoom). Depending on your shooting styles no right or wrong on which to get first.
Given the availability of the pro zooms these days I think the prime route is outdated and not really necessary, though I do feel that it is still the best way to learn photography.