After this long comment discussion on Facebook about smart irrigation controllers, I purchased the RainMachine Touch HD-16, which was really easy to set up. It talks directly to the weather station on my roof (an Ambient Weather WS-1002-WIFI OBSERVER) for super-localized data (via a Wunderground API key). If you don't have a weather station, it can also talk to regional weather stations, or connect to a rain sensor.
I walked around the yard turning zones on and off to test each sprinkler head. I'm going to have to water a lot until the [mostly-native] plants are established; hopefully, they will require very little water after a season or two.