His life in your home as a pet will be much different than being in a breeders home with many cats and possibly strangers coming and going. Some cats don't enjoy being in a crowd and there is probably a lot of activity going on at a breeder.
I would keep him confined to one room initially and spend bits of time throughout the day with him. If he likes treats, bring him a treat or two every time you go into the room, if he likes toys, use that as a bridge. Spend time in the room with him reading to him or talking to him with no expectation of touching or petting unless he comes to you. It is important for your children to do that too so he has an opportunity to observe them and get used to them as well. Patience and time is key. One of mine was/is very shy and another was very aggressive about being touched. With both patience was the key.
My Bengal is a retired queen and she was "shy" according to her breeder. While I don't disagree with that assessment, i see that she is more interested in doing her own thing most of the time that shy. If you aren't her chosen activity, she disregards you, shys away from pets, and goes about her business. She also watches for a while before she dives in to an activity or a group of people.
It is fantastic that you are willing to take an older cat. In my experience older cats take a bit longer to fall in love with you, but once they do all the time and work becomes worth it.