You absolutely have to start with Fort Lauderdale Beach Park, where you will find excellent parking (if you get there early), a huge number of shady trees, and grills & picnic tables for anyone to utilize.  There are no beaches like this one !

For number two, it is a bit of a tossup between Hollywood Beach and North Ocean Park, but I guess I would recommend Hollywood Beach. They are both off the tourist path, and are very family friendly. Use Google to investigate their unique characteristics.

For third, I would suggest Delray Beach, this is a bit north of Ft. Lauderdale, but it is a nice sized beach with restaurants in the area, some shopping, and it is off the beaten path. 

Lauderdale By the Sea 

Hollywood Beach is a super busy area! But it's fun. I love walking down the boardwalk there, it's so cute! Lauderdale By the Sea is a cute, family area. The beaches are very clean here, it's one of my favorites! Dania Beach is much more quieter than the rest of the beaches. Very tranquil actually :)