A father who wants to bless his family, whom should he bless first? His wife? His oldest son? His oldest child? The oldest among his sons, daughters, sons-in-law, and daughters-in-law? The cohanim? The b'not-cohanim?
I assume you mean traditional Friday-night blessing before kiddush? Or in a Mi SheBerach blessing after being called up to the Torah? Either way, I'd say birth order.
My impression is this is a matter of custom; it would be a stretch to apply the priorities in Talmud Horiyot (Cohen before Levi before Yisrael, but scholar trumps all), as that's for opportunities open to anyone; this is simply your children. To order it any other way is begging for fights in your family. "Shmerel you're the oldest, but I'm giving the bracha to Berel first because he's a scholar and you're an ignoramus"? I think not!
Jacob's blessings to his children (Genesis Ch. 49) is more or less in birth order (and the commentaries there address the deviations), though his daughter Dinah isn't mentioned as the blessings pertain to their tribal offspring (which is patrilineal).
My strong inclination, simply based on what I've seen, is to go in birth order, oldest child to youngest child, regardless of gender. (Or if your custom is that mom does blessings too, she could have some Cohen children and some non-Cohen children, from two different marriages -- I'd strongly, strongly advise simply going in birth order.) Do parents bless children-in-law? I can't say I've seen it done, though I don't see the harm. Then you get to the question of how to treat children-in-law; some families like photos of just their children, no spouses -- some would consider that horrible. What I see in Mi Sheberachs -- as well as in passing-around-the-kiddush-cups (among those who do a fancy order for that)-- is: my oldest child, then his/her spouse; then my next child, then his/her spouse. Grandchildren? Eh, I'd make the next generation wait till after the current one is done. (Though mi sheberachs usually do "my oldest, his/her spouse, and their offspring ...")