Generally two (or one, or three, if I've got less/more digging in mind, in advance) of my initial founders are set to be dedicated miners, never intended to do anything but that. If, in a later migration, significantly good miners arrive with some other experience that I find useful, I may give them mining but occasionally draw them into the other task. This would need a high level (say 6+) of this other skill, and a mining skill significant enough not to be worth ignoring in favour of this other skill. Lower levels of military experience might also tip the scales, given the principle later espoused about military/civilian mixed dwarves.
One dwarf is given the social skills to become de facto expedition leader, and usually also broker/manager, but not always. If not brokering and not managing (and not just generally 'leading') this dwarf may be given some job such as stonecrafting the trade goods, but won't be specifically given embarking skills in that non-vital job for it and will train up from zero.
All the rest of the embarking crew are given a mix of the vital jobs. Those may well be Carpenter, Mason, Planter, Brewer, Wood-cutter (if the map suggests that making a trained one), and the like. Mixed according to the foresight I have into the map, what psychological tendencies each dwarf has (much as I did in choosing the miners and proto-noble, above, together with preferences), how much I want to experiment, what I might intend to do with this embark, etc.
Usually the miners end up with max mining only (5/10 enhancements), the administrator is novice in all the social skills I put upon him to use up all 10 enhancement units, the others end up with either two or three different skills adding up to 10/10 in the enhancements.
When it comes to immigrants, if the embarkation mason has practised enough, he probably will retain his position. But if he doubled up as brewer, had not yet done quite so much experience-building masonry (e.g. block-grinding) and he has a significantly competent rival arrive he might find himself doing more brewing than he might have expected, and being removed (at least officially) from the masonry team. The same with the other embarkationers, if new arrivals instantly out-shine them. However, the ex-mason would probably be asked to join in with the construction of masonry (as might any other unoccupied dwarf, plus anyone else I can spare if something needs building right now!) outside of of anything quality-level related.
In a way, that's the pattern for most of the skilled works. I will generally have only one dwarf (the best skilled one) on stuff like armorsmithing and weaponsmithing, but that doesn't automatically excuse them from other jobs that they also have an aptitude for, and may be enrolled into smoothing, masonry or even plant gathering if their major skill or skills cannot be immediately used.
Hauling is generally turned entirely off for miners and for any worker who has the kind of job that needs-to-be-done-now, perhaps turning on a single hauling type (e.g. food, or refuse) if they would otherwise be idle and that category of hauling could use a bit of ad-hoc help. I tend to turn off burial from absolutely every dwarf, so as to more easily identify in DF the migration wave (although that's a redundant method now that I habitually use a nickname marker for each dwarf so far organised), although obviously I'd have to turn it on again for someone if actual funereal duties were required.
Utter peasants will probably have (barring burial) the entire hauling complement on, and may be enlisted into the masonic arts for structure assembly. Nothing that would give skill levels. I try not to get peasants to undertake necessary smoothing, because they then skill-up in that area and messes up my organisational ideas. Someone already with a skill (but currently idle) can actually do quite a bit of the old stone detailing before they lose their original profession colouration. (Even so, I do occasionally end up with a very good engraver who is supposed to be a decent brewer, instead.)
The military is another thing. My embarkation team very rarely get any look-in on that scene, although I might give them temporary opportunities to gain basic dodging if I'm feeling paranoid about attacks, as the fort progresses. But migrants with any military skills at all get looked at closely. Grouping those with familial collections with fellows in a similar position, I'll set up a unit (or units) to "keep them fresh" in their battle skills, and indeed improve them, but mostly as a back-up force. Immigrants with significant military skills but a uniquely valuable profession are also molly-coddled. Although for ease of use, these two types still get the same "on duty/off duty" cycle-length as the final set, who are the ones who aren't professional enough in any civvie job, nor romantically attached. They'd be my main phalanx. On top of the above three-way split, there's also splitting into ranged/melee and perhaps further down into two-person units for training purposes (although unwieldy when it comes to any actual battle).
Even the 'dedicated military' get to do something when not on-duty. Might be as little as hauling, might be as an auxiliary cook. I try to avoid weaponsmiths/armoursmiths being militarised, of course, but I'm not entirely so strict so they may be in the "Weekend Warrior" grouping, if not in the "Married Mob" one, if they do have usable military skills.
TL;DR; Using the Therapist, I will identify key workers, but need to deal with the in-game information regarding psychology/relations and sometimes make compromises. And sometimes need to remove them from other decent-but-not-important tasks in order to accomplish other tasks for whom they are needed (either as the primary, or as a useful auxilliary). Specialists rule, but you can't always get what you want. And two level-10 armoursmiths (one trained up to that level, the other popped up at random) cause me much grief. As do dabbling weaponsmiths who mood themselves up to legendary status just as I'd managed to train a better starting weaponsmith to that level through long effort, because in both cases I'm probably going to ignore (although at least keep in reserve) the lesser skilled of the two's extensive contribution to that field.