I know that everyone says a newborn is best, but I will tell you now that anyone will adopt a newborn. That 3-10 year old will truly be able to appreciate what you did for them. You have to remember that adoption cannot be a selfish choice. No matter what your choice is, just be sure to remember you are making a commitment and providing a child with a family.
Statistically, 3-10 year old's or "older children" as their known by foster parents and systems have far less chance of being adopted than an infant. Most of them will spend the next 5-10 years in foster care and when they become teenagers, many will end up in group homes until they are 18. I was one of the lucky few to be adopted at the age of 4, and my parents would have adopted my older siblings (6,8,9,12) if they could, but they didn't have the same father so it didn't work.
Two of them were adopted by one mom. One of those two was back in foster care in her teens. The oldest two grew up in foster homes.
I know I'm biased, but adoption is a very serious decision and you really should look into the statistics before choosing an easily adopted infant over a lass than often adopted "older child".
Infants are amazing and if you can't have one then I think adopting one is a very beautiful thing, but if you have had babies of your own, then maybe give a little kid a chance.