On my design, in addition to a desktop brwoser, I've decided to set three breakpoints to fit an iPad, and iPhones 6 and 4. If I set them a tad wider than the devices, it ought to satisfy every other gizmo.

The problem is, I've scoured the internet for the correct screen pixel widths (with the devices held upright) but I'm finding three or four different opinions; even Apple gives conflicting information.
Does anyone possess such useful info please?

Try this resource out Freddy:

http://www.kylejlarson.com/blog/2015/ip … sign-tips/

or

https://www.google.com/search?q=iphone+ … p;ie=UTF-8

Thanks, I did, and I still am as confused as before.
For example, an iPhone 6 has a pixel width of 1080. That cannot be possible, it would make the screen almost as wide as a 13" laptop! It also lists a browser size of 414 px, which seems more realistic. Is this what I should be looking for, the browser width?

https://www.responsinator.com/
The responsinator gives different devices pixels sizes

I feel the real point here is that it does not matter. The endless number of available different display sizes means that the design has to look good at any size. 'Don't design for a specific device, design for all devices' is the philosophy behind responsive design and easily possible using the width slider and custom breakpoints in RSD.