Cover artists, graphic designers – the masters of the thumbnail. Even though the books are the authors’ babies, the image translation is up to someone else. Someone we might not know. Someone who might not have even read your book.
First phase, don’t leave anything to chance. Find commercially free images to give the artists. Make a mock-up if you’re really nervous about the designer. Honestly, you’ll probably get a good read on them depending on how they respond to what you give them. Depending on the size of the press, you might get one cover or a selection to pick from. While the press I’m with generally does one, the artist I’m with worked with me to try to meet somewhere between what my publisher wanted and what I wanted.
When it comes to what sort of cover art I’m attracted to in visual only book shopping, I like eclectic. Solid colors that are neutral or generally darker catch my eye. People who aren’t models. I hate the idea that every main character fits the mainstream aesthetics. That’s just not true. This is why I love art done by fans. They listen to the authors. (It’s why there are so many movie/fan-drawn book comparisons with Harry Potter).
My favorite book cover (besides either of mine) would be original screenplay for Fantastic Beasts and Where to Find Them. It’s dark blue with metallic inlay. The beasts are hidden throughout the inlay. My author art wept at the sight of it. I believe it is the international cover, but I’ve only check USA and UK.
To sum – cover art can be controversial. Whether we like it or not, the cover is what most readers see first. It is what draws them in. Start out on the right foot and give as much info as you can, and you’ll be fine.