You have to be careful with both rocks and rhode Island reds because most of the local ones are hatchery birds which are mixed and not true to the breed. Not that a little mixing is bad for egg laying but it is if you want a bird with a great personality.
There are a few standouts as far as great birds to handle and especially since you have a child. I'm sure there'll be others that will add to this list.
Top all time docile breed is a Speckled Sussex. I've had other Sussex but to date they aren't as docile. These girls are lap babies and great layers. Downfall is they are a little tougher to raise until the reach a certain age.
Next would be Brahmas. They lay huge eggs and I've never seen an aggressive one. They do like to go broody sometimes though. They are probably my personal favorites.
Third would be Orpingtons. They are also very easy to become lap babies and lay big eggs. In this case however I recommend you steer away from hatchery birds and go for breeder birds. There's a huge difference. Once in a while you will get an ornery rooster but since you are just wanting girls you should be okay.
Another breed that is very docile but harder to find a Salmon Faverolles. Their eggs aren't quite as large and they don't lay very many.
Heritage barred rocks seem to be really great dependable layers but I've found hatchery ones are a bit cranky. Rocks will give you the eggs but might not be a lap chicken.
I've heard Ameraucanas are great birds but often easter eggers are called Ameraucanas so you have to know your breeder.
As far as pullets go if you pick up one for $15 that is old enough to sex that is a good price if it's a decent quality bird. If it's a young barnyard bird you would be paying too much in my opinion if it is still young.
I'm can be a bit of a bird snob. But it all comes down to this: If you enjoy what you have then whatever labor that comes along with it is worthwhile. If you don't enjoy looking at or being around your chickens then, feeding , watering, collecting eggs, etc becomes work.
And let me tell you it's really hard to enjoy that in this weather!!!