I'd always assumed that legitimacy would be primary, but that's just an assumption based on English law (solidified by recent reading of Ang's Hands of the King). Longevity/prophecy runs in the Numenor bloodline, so dilution by non-Numenorean non-spouses would reduce the value of the stock -- as of course would marrying someone from Rohan. (I still periodically wonder what Denethor would make of his son marrying Eowyn.) The stewardship & the Ithilien princedom might of course run separately from each other, & from Faramir's material possessions, with Aragorn potentially assuming the right to appoint the steward from amongst Faramir's family.

And I really ought not to be mulling all this atm...