I honestly mostly just want to know about the card stock and size. I know that there are people who care deeply about what system the artist based their deck on, blah blah blah, but I'm confident in the way I read cards so either I respond to the art or I don't. The artist can have no background whatsoever in tarot and that is totally fine with me. Honestly, there have been times when I was ready to buy a deck but the artist was pretentious and a jerk to people on this forum (see my second point) and so I will never buy anything from them ever, no matter how much I like the art.
I do check to see if the artist is generally polite on social media, if they're on social media at all. That is actually more important to me. If the artist is on social media, I want to know what the agreed upon hashtags for the deck are, because I buy cards like I buy make up: I scroll through my instagram feed to see what the colors are like in a variety of non-professional lighting conditions. Of course, you can't do that with a super new deck, or one that's crowd funded and not out yet, but still.
I do like hearing a little about the artist's inspirations in a more general sense, or why they made a particular choice for a strange/refreshing interpretation of the card.
I'm all for self promotion, I love artistic confidence. But whenever a deck comes out and is like, "THE MOST IMPORTANT INNOVATION IN TAROT SINCE CROWLEY!" I just...uh huh. Nope.
So, basically, good art and being nice to people?

yes.
EDIT TO ADD: I checked your thread on the deck and everything I would want to hear is basically there. I, personally, love knowing when a deck is being made by someone with a design background (not all artists are designers and there is a palatable difference when an artist is both and cards are a product, after all, and they benefit greatly from a designer's touch) and I love love love hearing a creator have the confidence and desire to make a luxury product. BLACK EDGING? I'm so there.