Hi,
I will start by saying "I am very sorry for your loss", that is a very sad story but also a very warming thought that you would take your children to the "Happiest Place on Earth" as you had both discussed. When you check in at your resort, make sure to ask for a button that says "My First Trip To Disney World". These buttons are complimentary and if you wear them during your vacation you will most likely receive some "special" attention.
I would recommend one of the "value" Resorts as you mention you are on a tight budget. These are nice accommodations for the price and also have that wonderful "Disney" themeing to them as well. I don't think you can go wrong with either of them as they are all very similar (just different themes mostly), there's the All-Star Music, All-Star Movies, All-Star Sports and the Pop Century Resort. Please view this
link for information on each of these resorts. I would suggest that if you are flexible that you go during the off-season to enjoy the lower rates. Typically, the "value season" would be after New Year's Day until mid-February; August and September; and after Thanksgiving until Christmas week. Being a resort guest you will also get many benefits such as, complimentary and unlimited Walt Disney World Transportation, Extra Magic Hours at the parks, you can have your purchases delivered right to your resort at no extra charge...this is especially nice as you have 3 children and do not need to be lugging around all kinds of extra packages and such!, and many more benefits...too many to list with my limited word count. Oh, and the most important benefit is being surrounded by that "Disney Magic" 24 hours a day! The value resorts are centrally located to all of the parks and are easily accessible. I hope this helps you a little to plan your magical trip.
Best wishes,
Brigitta