The iPhone has a Do-Not-Disturb feature that will mute all text and notifications and allow calls from those on a list that you can specify. Something to think about if you can tweak it to the way you desire without interrupting too much other...
Great question. To clarify, are you trying to have it so the text message only vibrates and never has a notification sound? If so, you can go to Settings>Sounds>Text notification and choose none or any other option you would like.
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