phone vs watch notices

I just got the Apple Watch yesterday, and I am trying to figure it out. I would like my phone to still make the message alert sound and my watch to only buzz/vibrate as the message alert. I have noticed that when they are near each other my phone does not make the message alert sound. I am also hoping that when I turn my phone on silent, that then my watch still only makes the buzz/vibrate alert and does not make a sound.