In some respect you are violating the principles of responsive design doing this. Now, if your minimum width is so small that no one will ever reach it then it doesn’t matter. But if this is the case then why even have a minimum width? By adding a minimum width you are basically imposing a restriction on your viewers that probably doesn’t need to be there in the first place.
Here is how I would do responsive design. Narrow your browser as skinny as it will go and style your page to look nice in that narrow view port. Use this as your base styling. There is no need to set minimum widths here. If the device the user is viewing your page with is too narrow then their browser will supply a horizontal scroll bar if needed.
After you have the skinny styling in place then gradually widen your browser and once you think you have enough horizontal room to rearrange elements on your page then set your first break point there and style the changes under that break point. Use
em units for the break point (that way it will take into account not only changes in view port width but also changes in text size). To get the approximate
em units just divide the
px width by 16. Continue widening and adding break points as needed.
Now while I don’t recommend you set a min-width on your page I do recommend you set a max-width, and use
em units for that as well. There is no one rule here but a lot of people start finding content hard to read if it extends beyond the high 40’s