Rats are a worry for chickens in general, especially chicks. Every now and then I myself have a rat issue. Thankfully I've never lost a chicken or chick to one. I cannot put out poison as there are too many cats in the neighborhood along with fear of my chickens finding some way to get into it. My rat solution is CeeCee. Forget cats keeping vermin down, nothing beats a good ratter. Rats is not my issue at the moment though, possums are invading again. CeeCee got another big one last night. Darn thing was feasting on eggs dad forgot to collect. I do not know why, but, spring brings those things off the hill and into the backyard.
Vermin issue aside, either breed would do well for you. Whose to say you cannot have both? I have not had person experience with bantom cochins, but I do have the big bowling ball girls. They look huge, but it is a illusion, they are all feathers. They also lay smaller eggs. Not much bigger then a silkie egg which was shocking at first considering their size. My 2 are prone to broodiness, but nothing compared to the silkies, or my Marans or old Momma Hen to be honest. I do hear bantam cochins are worse though. Truthfully speaking, I like my cochins, they are pretty but I spend the majority of the summer ready to strangle them. They are my egg eaters and if Rosie and my grandmother had not fallen for them they would already be chicken and dumplings. Grandma is gone but I cannot make myself get rid of "her" hens. When they are gone I doubt I will replace them though. This just means they will be like the ole bat Momma Hen and live forever.
Silkies, I cannot say enough good things about silkies and I highly recommend them. You want broodies, check. You want child friendly, double check. You want little clowns whose antics will have you laughing....triple check. Silkie zoomies, enough said. When they are not broody they are very reliable egg layers. Broody raised or hand raised even the most standoffish silkie chicks will grow up to be little nosy busybodies who want to be in your business and lap. I have officially now even won over Barbosa and Davy who were not handled that much and skeptical of me when they first arrived. Silkies will need a little more care then a cochin but it is very easy to do. If they free range, they will need their crests trimmed so they can see. People often say silkies are dumb. No, that is very much not true, they are wicked smart. They just need to be able to see. In the winter is when they really need extra care. All they need though is a draft free dry coop. But all chickens honestly need that and should be given that. In the fall just insulate you coop with a tarp and keep it clean and your silkies will be good even in frigid temps. Kentucky can get bitterly cold and mine do just fine. It was my silkies who had a blast in the snow while my other birds protested the white lava and thought it was going to kill them.
Don't know if there is now access for small flocks (i.e. small vials/few doses) readily available or not.....but @RoyalChick would also have to be comfortable vaccinating them herself, too. IDK if she is or not.
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hilarious! 
