Preferring a child over a mistress?

Of course. There is a positive commandment of Kiddushin or it is a mitzvah. In any case, the best course according to the halakha is to perform Kiddushin and not live with a concubine. There is a debate among the poskim whether concubines are a prohibition and to what degree (torah?). But it is clear in the halakha that Kiddushin is the correct course. https://he.wikipedia.org/wiki/%D7%A4%D7%99%D7%9C%D7%92%D7%A9 Regarding the children's parentage, in principle there is no difference. A child from a mistress is of course not a bastard. Regarding priesthood, I assume that there is a presumption of majority in such a situation (if they live together as a couple). But I haven't checked it out to the end.