#1: Don’t worry too much about what to read to your kids, but read to them! And once they can read, make sure they never run out of books.
I started to make a list here and then decided that I probably can't do much better than these folks (though I'm tempted to make it into something a little easier to take to the library and tick off as you go...)
Though I will add the book I gift the most: A Child's First Book of Poems
— it has wonderful illustrations (by Cyndy Szekeres) which I think was important for me in interfacing my young mind with the magic of poetry in a really positive way.
It's out-of-print, so I buy it used and for whatever reason, there are two separate listings on Amazon:
This website is where a friend chooses books for reading aloud: