Reading that this is you 1st trip, first of all congratulations!!!! If you are like many of us on the DIS it won't be your last! As it is your 1st I would definitely do your research. Get each kids top 2 or 3 must do's while at WDW and plan accordingly. Don't plan each minute or "commando plan" as some call it but plan the day as far as this day we will be at MK, tommorrow Epcot, etc. Be willing to change your plans!
Dining plan was 1 table service - sit down meal, 1 counter service - think McDonalds Value meal with dessert, and 1 snack credit per day. All credits are totaled at the beginning of your stay and can be used as you wish - 2 snacks in 1 day, 2 table service in 1 day, etc. At the end of our stay we had 16 leftover snack credits and got stuff to bring home with us - rice crispie treats, waters, and such. At table service there was so much food we often asked them to package desserts to take back to the hotel with us - they always did this with no issues. Also, remember counter service comes with a dessert as well and we brought home several prepackaged brownies for later consumption.
As others have posted you can make your reservations 180 days in advance and certain reservations will go that fast - but do not give up if you don't get them on the 1st shot, people cancel and by calling repeatedly you can get those ressies. When we went it was CRT for the Princess breakfast - and I think I called 30 times before I got it.
Visit allears.net and browse through the menu's. This way you can totally cut out some restaurants while finding some restaurants that you feel fit your style. Don't go for the most expensive go for what you like!
Do you have to make every reservation? No, I don't think so but if there are particulars that are a must do...a certain character meal, a certain restaurant... then I would definitely make those reservations so that you KNOW you can get into that place. When we went Disney was doing a special promotion and most of the restaurants were completely booked and unable to handle walk ins. But we did get a seating at Whispering Canyon Cafe w/o prior reservations so it does depends on where.
Plan on eating where you are going to be that day. Alot of people waste alot of time because they planned on eating in Epcot when they are spending the day in MK. Now if you are splitting the day between 2 parks anyway, fine but to go to another park just for Dinner you'll end up wasting alot of time better spent on the rides, shows, etc.
Most of all relax and have fun. Take lots of pictures and enjoy seeing WDW through your childrens eyes. It is truly a magical experience!!!