Congratulations – – sounds like an exciting project! And congrats on the expanding family!
Lutron Caseta now officially works with SmartThings, and people are reporting that the integration is quick and smooth, but it is cloud to cloud so you will need the Lutron SmartBridge to make it work. See ( this is a clickable link)
As far as button devices, there are quite a few options. The following FAQ has both handheld and wall mount models:
Regarding dimmer switches, different things work for different people. The following thread discusses the various features that different devices might have and why you might like one over another. The light switch discussion starts around post 40.
You might also take a look at the quick browse lists in the community – created wiki under project reports and look at the list for “whole house projects.” That might give you some additional ideas:
And congrats on the expanding family!