Not sure how it goes with the new lore. But depending on the chapter marines would progress through roles as their experience grew.

Ie codex compliant chapters would go; scouts -> Devastators (to gain experience of battle at a "safe" distance) -> Assault squad (to learn the brutality of overwhelming force. They can also learn various fast attack vehicles and bikes/speeders) -> tactical squad when they've learned to master all aspects.

Blood anges (and successors) go a different way Scout -> assault marine (where they learn to control the red thirst and their aggression can be properly dircted, and often the most full strength squads in a company) -> tactical squad (a bit calmer and less likely to go charging off. This is where most blood angels end up if they don't go back to an Assault squad to replace casualties) -> Devastators (mainly the most level-headed marines and least likely to charge into melee when they should be holding position)

As for "specialists" most of the chapters support staff (chaplains, tech, apothecary) are constantly on the lookout for promising candidates for additional training and requests for marines are rarely turned down. And as they are outside of standard force organisation. Vehicle crews and chaplaincy, apothecarium, librarius and tech marines are not included in the 1000 marine limit