Breeding stats question:

So I have seen a lot of posts on breeding and I still don't quite understand it. The parents pass on their stats that they have currently or the stats they had right after being tamed?

Do I want to power level the parents to max level THEN breed them?

Also people will say 30+ or 40+ what do those mean, is that an increase in levels?

Sorry for my ignorance but I would like to get into breeding.

(Edit)After a bit of looking I found a great thread for this breeding guide