Which is most used Barrel Connector ID? 2.1m or 2.5mm?
Alas, this is difficult to pin down. "Most used" depends on your industry, your region of the world and the year you ask the question.

For a long time every manufacturer would pick their own and supply the plug to suit. Consumers who tried to connect their own would quickly discover they'd fried the appliance by connecting the wrong voltage to it. So people learnt to limit the mixing and matching of supplies and devices, and manufacturers were motivated to pick uncommon sizes to prevent misconnection.

It's probably only since the Arduino that there's been much interest in supplying your own supply, and the question of compatibility became of general concern. The Arduino happens to use the 2.1mm barrel jack, and the Beaglebone followed suit.

So 2.1mm has become a de-facto standard in the maker community, which has influenced a lot of electronics. But this is neither official nor stable, so I'm afraid your goal of "maximum compatibility with existing PSU around the house" is probably largely unachievable in April of 2019.