I think your interpretation is okay .... so far. The thing is, to start off with some type of basic understanding and then build on it. There are a few models for this basic understanding. Once one begins to build on it, it becomes a template. In a way, one can then develop 'multiple bases' of understanding so one can use the basis of the Tree for gaining comprehension about many things.
" Let me rephrase what I have understood so far: the sefirot are different characteritics of God, that we can experience or see in our lifes, and the goal in life is to reach a point where we experience them all. "
I think the 'see and experience ' first comes as a progression of understanding each phase (Sephiroth). Next comes the comprehension of how they all come together and work together to create any whole system.
One thing to bear in mind is there is more of a 'traditional approach' via or with influential aspects , of Judaism - like your definition above - the other is more modern and western and relates to tarot, enumeration, and concepts we may understand better in their classical western form ( like the 4 elements ) and number progression from 1 - 10, and correspondance systems ( as in 777 )