In everyday business, I would generally start with the day and then follow with the month if it's relevant (often it's not, if talking about a date in the near future), and finally by year if needed. I can't imagine when I'd start with the month, really, but that might be because in Finnish you'd almost always say and write dates with the day first.

As far as date formats go, apart from the ISO format, "21 Jul 2020" is definitely my favorite and always unambiguous. The only downside is that it's language dependent.