Welcome!
I think the first thing you need to decide is if you will stay on site or off. There are benefits to each and it really just needs to be a family decision. Off site would allow you all to stay in a house together with a kitchen that would save on meals etc. But, you would definitely need to rent a car and would not be eligible for "resort guest only" priviliges while in the Disney parks.
Staying on site, with your numbers, will limit your options. You can stay at at a Value with two rooms or at the family suites at the Value resort. Two rooms at any hotel will work for you, but if you need to keep the budget under control, a Value resort may be the only ones affordable. Fort Wilderness has cabins that will accommodate your family and comes with a kitchen. You may want to check that out as well.
Another on site option is to rent points from a DVC owner and stay in a two bedroom villa. I know very little about this process, so someone else will have to chime in with the details.
Once you've made a choice about lodging you can move on to other things. You'll need park tickets for each family member. You can save a little money by choosing tickets that don't allow you to park hop and that expire at the end of your stay.
Next, check out Disney's Dining Plan. You'll find a lot of info about the
DDP on this board. If we (me, DH, 3 kids) were staying in a hotel and not prepairing some of our own meals, the DDP would be a great deal for us. If you are staying on site, flying down and not renting a car, you can have groceries delivered to your resort. You can also ship a box of nonperishable snacks from home prior to leaving and the resort will hold your package for your arrival.
HTH
Good luck and happy planning!