I have a 7 year old and a 9 year old, so we tried to get breeds that would be good with the kiddos too. We also wanted to pick breeds that would be good layers, not flighty, and able to handle both hot and cold (though not, like, Canada cold, because we live in northern Florida)... We ended up getting one each of the Buff Orpington, Black Australorp, Barred Rock, Golden-Laced Wyandotte, and Delaware. If we had gotten a sixth, we would have gotten a Speckled Sussex, as they also have the reputation for having all of the qualities we were looking for (and the experiences of a good friend of mine back that up). With little kids, expect that each chicken will have a name, so I recommend getting one each of multiple breeds to make it easy to tell them apart -- this has worked very well for us.
Now, our chickens are only 6 1/2 weeks old, so we haven't had them very long, but we got them as day-old chicks from My Pet Chicken; they were less than a day old when we got them, and we have handled them daily since then. In our experience, the Buff Orpington (Stella) is the sweetest chicken EVER -- she loves to be cuddled, and even to sit on my daughter's shoulder. The Black Austrolorp (Pepper) and the Barred Rock (Henrietta) will run when you try to catch them, but are easy enough to entice with treats -- they eat right out of our hands, and once we get them calm, they will gladly cuddle for a bit. Our Wyandotte (Lynda Carter) is a bit more stand-offish -- she tries to fly once we catch her, and is not overly fond of cuddling, though she will eventually perch for a bit on your finger (and will stay longer if you have treats). Our Delaware is the same as the Wyandotte in temperament, but is getting more stand-offish as time goes on, but we are pretty sure that is because SHE (Gwenny Henny) is actually a HE (Lenny Roo... oops!)...
Everybody I know who has Orpingtons and kids swears up and down that they are the very best for little children. From our brief experience of chicken-keeping, I would have to concur. We have a Buff Orpington, but there are other varieties as well -- one of my friends has a Chocolate Orpington and she is beautiful! Of what we have, the Black Austrolorp would be my second recommendation, followed by the Barred Rock (with the one caveat that the Barred Rock is slightly more jumpy, so really needs to be handled daily, not only for the chickens sake but also for the kids. My Wyandotte and Delaware would be fine for your oldest, but maybe not for your youngest, although they are quick enough that the youngest even catching them would be a challenge.
My friend who has the Chocolate Orpington and the Speckled Sussex has an 8 year old and a 6 year old, and both of those chickens are great with her kids... the Speckled Sussex was great with mine as well when they met her.
The one breed I have any experience with that I would definitely recommend avoiding is the Rhode Island Red. My uncle had a flock of these and they used to chase people and try to attack them... especially small children. I know other folks who have not had those experiences with RIRs, but seeing my daughter running in fear from a flock of angry red hens was enough for me!
There is a new book that came out recently you might want to read with your oldest. It is called "A Kid's Guide to Keeping Chickens" by Melissa Caughey. I borrowed this from my local library when it first came out and read it with my kids. It was a really great resource for all things chicken, and it also has a section on recommended breeds, their characteristics, etc... It was very helpful for us, for selecting breeds and preparing, and also letting the kids know what all is involved with caring for the birds when they arrive.
Good luck on your chicken journey!! And welcome to BYC
