When is taxonomy appropriate
Taxonomies are best used to define properties that:


are shared across multiple content items;
need to be grouped with similar properties.


For instance, if you're selling t-shirts, the taxonomy terms 'blue', 'red' and 'yellow' are grouped in the 'color' vocabulary. By tagging all t-shirts of the same color with the same taxonomy term, you define a relationship between those t-shirts. This makes it very easy to generate a page showing all blue, red or yellow t-shirts.

Taxonomy terms, like many other entity types, are 'fieldable', which means that you can add fields to them to contain data. For instance, if you add an image field to the taxonomy terms in the 'color' vocabulary, you could define an example image for each color term.

If this example with t-shirts and colors matches your use case, then the answer to your question is: Yes, taxonomy is the Drupal way to do it.

By the way, the word "entity" has a very broad meaning in Drupal. 'Taxonomy term' is a type of entity, just like 'node', 'user' and 'file'. Saying that "entities will do what you need" is like saying "building materials will allow me to build a house". It's a statement that (almost) can't be wrong. You need to answer the question: Which type of entity is best to solve this specific problem?