When we go to the butcher's shop, which color meat should we choose? Cherry-red or brownish-red?
The color of beef and other meats is actually a pretty big topic.  It is influenced by the animal's diet, the particular breed, how much the muscle was worked, how much the meat has been exposed to oxygen, and how fresh it is. The USDA and other agencies put out articles about it, and it's widely debated which is "better".

There are some stores that will intentionally keep meet away from oxygen until it is displayed and then introduce oxygen to have the meat "bloom" so it looks particularly red, but this reduces its shelf life. It would actually be better to buy beef that has not bloomed and is more purple in color because it's likely to be fresher.

Another aspect for beef is the fat.  Studies have shown that grass-fed and free range beef has higher nutrients (which is why you see so many "grass fed" labels), and this causes the fat to take on a yellow color. This meat can have a much stronger flavor, and is sometimes gamier and a little tougher, even though it is more nutritious.  I prefer this kind of meat but some people don't.

I have learned to pick meat based on its appearance and the color is just part of it.  You learn to determine what looks fresh and does not, it's the color but also the sheen, how well it "stands up", is it flopping or falling apart, is there any kind of sheen on it.  There is a difference between the gray color you get from oxidation and the beginning of spoilage, and naturally darker colors of fresh meat. I will sometimes have the butcher flip it over so I can see both sides, they will of course put it in the case with the best side showing and if it's been sitting a while the underside may show that it is gray and starting to lose its freshness. I hate it when I buy a pre-packaged steak that looks good and bring it home and flip it over and it looks like it's several days old.