Australians say, "Good luck on the day" meaning that they wish you luck for that special day in the near future. They may also say, Good luck for the exam today/tomorrow".

Sometimes for non-native speakers, the shorter the better. Here, let me suggest: "Best of luck." or "Best of luck to you." If you get into the habit of saying, "The very best of luck," all of the time, people will realize you do not vary the degree of well wishing and might think you come across as insincere.

Both are right, but the americans prefer to use "the very best of luck" And it doens't matter if you use or not the particle "of" in this case. Like I said, both are right

"the best luck on your big day!" is just plain WRONG. You can say: 1. The best OF luck.... 2. The very best OF luck....