Well, that's one thing you could choose:
How big is the pool your migrants come from? And do they all come from one place, or from several different places?
Maybe, in one game, there isn't a Mountainhome at all, maybe the dwarfs all live in ghettos and small forts, and your job is to found a Dwarf Nation.
That choice alone could effect what migrants you get, and also what Nobles you get. If there's no centralized Dwarf power, then maybe all the Nobles that arrive in your Fortress are ones without Noble titles like the Dungeonmaster and the Philosopher.
You'd then be able to decide for yourself (or your dwarfs would elect) who's a Baron, who's the King/Queen, etc. from among your own dwarfs.
The tradeoff to this is, you wouldn't have a powerful dwarf trading partner, so dwarf caravans might not bring much. You'd also be expected to send aid to the other dwarfs on the map. You wouldn't be able to rely on the Mountainhome for military aid, when the Army Arc comes in, since you're the Mountainhome.
The new genetic things coming in could go well with this, too, since you could maybe choose which Clan each of your 7 came from, and each Clan might have different genetic traits. You could then choose what your dwarfs' relationship is, with the different Clans (since they might also be powerful political entities), as well as with the Mountainhome.
If that caused you to have a good relationship with a Clan, but a bad relationship with the Mountainhome, you might end up part of a dwarf civil war, or you might end up founding a dwarf nation, as above, only one that's separate, and opposed to, the Mountainhome.
You might, alternatively, end up recieving migrants from your Clan, who are on the outs with (or criminal refugees from) the Mountainhome, causing you considerable strife with the Dwarf King (meaning a blockade on the Dwarf Caravan, more and worse Nobles, less and worse Migrants, no military assistance, etc.), and the challenge of "healing the rift" that's weaking the Dwarf people.
Another alternative to this is that you might have to hide refugees from arriving Nobles, who have been sent by the King to put your Fortress under their thumb (which leads to more hammerings than usual, demands for traditional dwarf items, etc.). Or they might be from the Clan, and plotting to use your Fortress as a staging-point for their insurrection (which means they'd order lots of weapons and armour to be made, and might send your soldiers off to fight, with the Army Arc.). Something that you, as a player, might not want happening, and would then have the challenge of preventing.