I agree with doing the "make viewport narrower" approach (design for desktop first) though some prefer the "make viewport wider" approach (design for mobile first). It's only a matter of preference and what works better for you.
Basically I design so it looks good for desktop. Then I narrow the viewport. When I see something cramped or sticking out of its container element where resizing, wrapping or overflow is not acceptable, that's where I put a break point. Then I continue to narrow the viewport until it breaks the design again. Rinse repeat until it gets down to the narrowest probable width.