In your post that started out this topic, you listed yourself as being a “hobbiest.” So I’ll answer your question assuming that’s the case and that you’ve had minimal formal training.
Most formal university design programs (at least here in the U.S.) don’t start out with projects that try to imitate real-life, professional projects. Those kinds of projects, like logo designs, typically aren’t assigned until the 3rd and 4th years.
The reason for this is because there are lots of prerequisite basics that need to be learned before diving headfirst into realistic projects. Most of these basics have to do with a loose collection of principles typically known as the elements of design. These elements or principles involve learning about and working with color, shapes, negative spaces, texture, balance, contrast, rhythm, harmony, hierarchy, etc. If you look up these things, you might also want to look up Gestalt psychology since it helps put into context why these elements are important.
Concurrent with a focus on these principles is a strong emphasis on typography. The reason for this is because, first, typography is a huge part of graphic design and, second, typographical forms are a microcosm of all the elements of design boiled down to their bare essence into letters, numerals, various marks and, in combination with each other, words.
So to answer your question directly, I think a beginning designer should concentrate on the elements of design and typography. Outside of a formal program, though, most designers typically want to skip over the prerequisites and jump directly into those things that piqued their interest in the subject to begin with. This is unfortunate since it leave huge gaps of understanding and ability that are difficult to overcome.