Hi R.,
I have been to Disney Several times with and without kids. Your kids are at a great age to go! As many people said in other posts. Some times in April can be peak season, so avoid spring beak weeks and Easter. Aim for the later part of April. April is also one of the best weather times to visit. Spring in Florida boasts perfect temps and minimal rainfall (around 3 inches)
August does tend to be less crowded towards the end of the month due to children going back to school. The weather also gets much hotter and humid (Hi 80's and some 90's) and the rain becomes more frequent, but if you're prepared you can use that to your advantage.
As others have mentioned there is a buy 4 get 3 free deal going on now. This applies to value resorts only. Disney does these offers to fill the hotels and parks; I would recommend taking advantage of it if you can. I did for my family of 4.
Disney has different levels of hotels. Deluxe (average $349 per night, moderate (average $149 per night) and value (average $89 per night) rooms accommodate 4. for 5+ you'll need to get a suite or an adjoining room.
I have stayed in all of the levels that Disney has to offer. If you can afford to splurge stay at a Deluxe resort. They are closer to the magic kingdom and offer great views at night of the fireworks not to mention easier access to the action. My favorite if the Polynesian. If you're on a budget as most of us are right now. The value resorts also offer that great Disney magic. The rooms are a little smaller, but still nice and you'll end up walking a little farther to get to the busses that take you to the parks. I recommend Pop century. It's the newest value resort and we found everything there to be top notch. I was very skeptical at staying there on my last trip because I had always stayed at Moderate resorts prior. We liked it enough to book if for our next trip this May.
I used the dining plan for the first time in 2007, and we found that it saved us a ton of money. There are different levels to this plan as well. We are going with the standard plan(which is recommended by Disney) Each day every member in our family gets 1 snack credit (can be used for small milk and cereal chips fruit...), 1 counter service credit(used at any place that serves fast food type meals and includes you meal, and drink and I believe dessert) and 1 dinner credit (includes the same as counter service but at a sit down restaurant. Kids meals include an appetizer as well) We saved all of our receipts. They give you one that shows the actual cost of the meal. We tallied them up when we got home and found out we saved close to $1000 on our dining by purchasing the meal plan. I think that's worth it. Yes, you sometimes do get too much food depending on where you're eating, but I'd rather have more than not enough. BTW, my sister just got back and paid out of pocket for her family of 5. One sit down meal alone ran them $160! That would have been just 1 dining credit. You can also use the credits any way you choose, in any order.
As for touring advice. You need to go with a plan. The first time I went to Disney(on my honeymoon) we had no idea what we were doing. It makes for a frustrating trip and is a waste of money. So you're already on the right path by asking for advice. the websites everyone has given you are great ways to find out what you want to ____@____.com your kids read the ride descriptions with you and make a list of the ones you really want to go on. as well as where you want to eat. and leave the rest for another trip. I highly recommend at leave a full 7 days for a first trip to be able to see everything.
Others have mentioned adding a park hopper on to you tickets. This allows you to go to as many parks a day as you want. This is good if you're going to be there 4 days or less. if your there longer, save the $$ and don't get it. 1 perk per day is plenty. You can enter and reenter the same park as many times as you like once, you ticket is scanned. I recommend getting to the parks BEFORE they open for what they call "rope drop" tour the park leave for an afternoon break and then go back for dinner and stay until closing. To avoid needing a vacation from your vacation make sure you plan 1 day in the middle of your trip that doesn't involve going to a theme park.
Also just because you're staying at one type of resort, doesn't mean you can't "visit" the others. The fancier resorts have great restaurants. You can use your dining plan at most of them. Make sure you make your reservations as soon as you can. You can book them 90 days from the start of your trip. So if you go in April, you can start making your reservations ASAP. On our first trip I had no idea that we we're supposed to do that and we ate counter service the entire time. We were miserable seeing that we had just gotten off the Disney cruise where we were pampered with wonderful meals whenever we wanted them!
I hope this info has been a help. Enjoy your trip!