I have been giving one piece of advice to new parents.
It grew out of a task I managed to complete recently after putting it off for years: I brought all the mini-cassettes I had recorded during the early stages of my kids' lives into a local service and had them transferred to DVD.
I don't know why I waited so long. I think I feared it would be an expensive disappointment, that there would be hardly any footage at all (because I knew we rarely used the camera) or that it would be of very poor quality.
In the end, I was right in that there were only a few hours of footage, but actually it was a wonderful experience to sit and view some scenes from my sons' early years, even if my 17-year-old refused to watch with us. (He cannot stand to see himself on camera, even in videos where he's a child.)
The point from all this is that I learned one thing from this experience that led me to a valuable piece of advice to new parents:
When you are shooting video of your children, don't focus solely on them. Make sure you also get footage of the important people around them in their lives, especially older relatives who may not be present or even alive when the videos are viewed. As cute as your children may be to record, you and they will want to see more of aunts, cousins, grandparents, and close family friends when you view the videos in later years.
Moreover, make sure you record plenty of footage of yourselves, the parents or guardians, interacting with each child. You will miss this if it is not there.
Finally, when you do shoot video, consider that you may not be able to remember their friends' names in later years—or your children may view the videos when you are not there to identify people. Therefore, say names of people in the shot on occasion. "Here's William from next door, and there's Aunt Rose waving in the background..."
I wish we'd been given this advice!