As far as "is the plan worth it," it depends on how your family likes to eat. You get one table service credit, one counter service, and one snack for each night of your stay for $38 per adult, $11 per kid over 2. Under 2 eat free at buffets/all you can eat and can eat off adult plates for free at other places.
If you like to go to at least one "sit down" per day and eat a counter service, it is a good deal. For us, it works. For my sis...who likes a character breakfast each day and a sit down dinner and almost never eats counter service, it does not meet the needs of her family.
ADRs are just like the old "priority seating" except that you can make them 180 days in advance of your trip. It is a good idea to schedule your meals--that way you know that you will be seated at the restaurant of your choice somewhere close to your preferred time. You can always try "walk up and wait." SOmetimes they can get you in, sometimes not. Sometimes you will wait 5 minutes, sometimes 2 hours. You can't reserve counter service.