Love the idea!
I run our boys (relatives) nuts over the holidays and they love it. We volunteer to ring the Salvation Army bell or carol at the nursing homes and take wrapped boxes of nice Kleenex. This year, the Wednesday before Thanksgiving we are volunteering just to clean and chop veggies for dinner at the homeless shelter downtown.
That's part of it; the season is for giving and not just money, but TIME, the time to carol and sing for the elderly or time to chop veggies or ring a bell. Talk about giving until it hurts, stand outside a grocery for 2 hours listening to two boys ring an annoying little bell while the Chipmunks Christmas CD plays, now THAT'S giving. ;-)
I love the basket idea you have, but I think it be wise to stay local and keep it in your community. It wouldn't be hard to find a less fortunate family or organization that is helping lend a hand right in your own neighborhood.
Maybe call the county and ask about a foster family that has several orphans, ask your children's school guidance counselor if there is a family in need, talk to your local community center or nearby churches, they could probably give you leads as well.
I bet your local mall will erect a large Christmas tree and on it will be 1000+ angels, written on each you will find a name, age and wish. You could pick one or two, go buy the item and take it back to the tree. This is called Angel Tree Ministry's and there is normally one in nearly every city. The back ground to Angel Tree is one or both parents are in jail and it helps support the children's current caregiver. Angel Tree workers go to the jail, talk to moms and dads and get caregiver information. Then the worker contacts the caregiver and gets two toys and one useful item idea per child.
We worked with Angel Tree for about 4 years, I was the chick at the mall, I wrapped the items and I took the items to the caregivers and got to tell children that even though mom or dad was "away" they loved them and wished them Merry Christmas. The look on a child's face when they opened a Barbie from Mommy or a Truck from Daddy, when they never thought it possible, IS what makes our Christmas. It's a high like no other.
Have fun with it; you and Gio are doing your children a great, GREAT service and giving them a priceless gift.