then you should choose your pull-up bar as equipment, right?

A pull up bar is the first thing you should get since it can target muscles that are hard to do any other way. For most other muscles you can find some other way to strengthen them just using body weight exercises.

For most people a pull up bar plus body weight exercises will get them everything they want: enough fitness for good health. If you want to win competitions you need the right equipment (different competitions need different equipment).

In my specific case, yes. But you could also flip it around. Maybe select some muscles and not select any equipment. They you can see what kind of equipment you might want to buy.