I vote for "DD/MM/YYYY" with "/" as separator.
Mostly it's because of how I think of dates. For example, for 19/05/2016, I think (and say) "The ninetheenth of the firfth, two-thousand-sixteen" or "Fifth May". Though that's mostly because it's the system I'm used to in Swedish. Lots of other languages work differently. I think English, Hungarian and Japanese all work in a MM/DD (e.g. "May's fifth") format in their spoken languages.
A lot of these formats seem to dominate in different parts of the world, partly due to local language structure.
Still, considering that the DMY-format seems to dominate, as can be seen here, I strongly recommend for that to be the main form. If we take a look at the different SCP branches, we'll see that most branches would fall under that standard as well (according to the map):
DMY:
- EN (Commonwealth countries incl. Canada; Philippines)
- RU
- FR
- PL
- ES
- TH
- DE
- IT
- PT & PT-BR
- VN
- UA
- TR
- CN (Hong Kong; Macau; Singapore)
YMD:
- EN (Canada, India, Southern Africa)
- KO
- CN (Most of China)
- JP
- DE (Austria; Germany)
- TW
MDY:
- EN (Canada, Ghana, Nigeria, Philippines, USA)
- FR (Guinea, Togo)
As can be seen, the DMY format dominates both in terms of sheer number of people covered by the system, and by the number of countries using it. YMD comes second, mostly concentrated in the highly populous East Asian countries, with it being the International Standard being a second argument in its favour. The MDY format, however, seems to be limited to the US, Philippines, and a handful of equatorial African countries.