What is a luxury minimalist logo?


Well, as the graphic designer who loves to develop such a 'luxury minimalist’ logos, I can tell that the name of a such logos comes out from the study of the trends, the theme, line of competitors and the time spent into that study.

The best program for logo design and why


Absolutely - Adobe Illustrator, because it has primitives, as line / oval / ring / etc., it has a simple functions aka effects, which can give you an unpredictable interesting turn.