i have a lot in my mind.. But 1 particular word of advice that still stands out until today and use it for my kids would be "Always stand up for yourself". And hopefully, my kids can use it for their own kids too.
My mom used to say, "That's not nice" if one of us said something bad about someone. It always made me stop and think about my actions. I don't have kids, but I still hear that echo in my head whenever I may be tempted to say something not so nice about someone. Now, I joke a lot about people in general....but my intentions are never malicious.
My mother always told me that my family were my dearest friends. I tell my children that family is the most important thing. I tell my grandchildren that their brothers and sisters are their dearest friends. "Family is the most important thing!" is the thing I heard all my life and it is still true today.
I know this isn't quite what you're asking for, but my mother used to say do as i say, not as i do... which i never agreed with and still don't as a mother... I would urge my son to do as I do, to learn from me.
And in shops i have caught myself saying to my son 'look with your eyes not your hands...'