Silence or turn off certain notifications during bedtime?

My android phone (LG optimus G) is some 4 years old so I'm considering something new. I've been getting more and more junk notifications that wake us up. I don't want to turn the phone off in case there is some serious weather alert. Is there a late model Android phone where I can selectively change notification settings for certain apps, or to allow notifications from only certain ones?

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