You'll learn a lot during a physics degree, which will help direct your choices afterwards. Personally, I started off in astrophysics, but during my degree, found I was actually better suited to nuclear physics, and changed direction.
Following on from your degree, there's postgraduate study to look at. There are some astronomy-related jobs available if you've just finished a degree, but most serious astronomy is academic research work, for which you'll need to go on to get a PhD and postdoctoral research positions.
Joseph recommends the following next steps:
It's amazing that you are dreaming so big! As a rule of thumb, the chance of success is higher, no matter what you desire, to get into the best organization/league. E.g., if you wanna play professional basketball, you try to get into NBA. Same thing, if you'd like to become an astronomer, you might want to work, or at least start, with NASA.
Therefore, I went to NASA's website and found this:
Good luck :)