Look into the value packages. You can get some good deals with rooms and tickets.
I'm also for staying on the property, it is really really convient. Also, what saved us a ton, was the Disney meal plan. It is appx $40 a day per adult and $15 a day per child (I think the boys will be considered adults). I know this sounds like a lot of money, but once you get into the parks you'll see that it is a real savings. You get 1 snack (popcorn/bottle of water), a counter meal (burger, drink, side and dessert) and a sit down (app, entree, drink and dessert) a day. You can change them up how ever you like. ie - you may not want a sit down one day, so you can use 2 counter meals (these are usally at the park) instead. You can use some of the sit downs towards character meals as well. We had more then enough food for one day. I can't tell you how many rice crispy Mickey treats I had in my bag. We had granola bars for breakfast and we were fine.
We ate in Italy at Epcot.
DH's steak a la carte would have been $40 - no salad, no drink, no side, no dessert. He got all of this in his sit down meal. You can only get this meal plan when you stay on the property.
I've never stayed at one of the value hotels, but I hear they are great. The kids only care about a pool really, and they have that.
Let us know what you decide.