Your feeling is very common among recent graduates.
You can always start by aiming at the ceiling and see if you can hit the sky, i.e. go for that dream position right at the start.
It is most important then to have a presentation and portfolio that can tell future employers specific things they can expect from you, so it is important to convey precisely what you would want to do with the company, what your strengths are etc. Even if your story varies a lot across employers, it is better than a generic approach that does not make you stand out.