Is the order Armp > AD > AS if one was to go all out one of these?

On what type of character?

For Ad carries the build is usually IE ---> PD ---> LW

However each Ad Character is different. Take Riven for example. Riven prioritizes AD and then Arp and will build absolutely no AS.

On the other hand, a character like tryndamere will rush PD and then get IE and LW.

TLDR; Depends on the character you are playing.

That's a good point. But those champs are easy to see which items matter most. Lee sin needs no AS because of his passive. How about for junglers, in general?

It completely depends on the champion. You can't stereotype it.

Someone like Vayne needs AS early on whereas Tristana has a build in AS steroid. You would be unable to generalize or give a proper answer without more information. Sorry ):

If master yi, get 3 phantom dancers ;]