I want to tell my coworker to stop shipping his personal packages to the office
Is that against company policies? Why do you need to tell him that?
I just don't want him to ship packages to the office.
There are some things that my coworkers do that I find very annoying as well, but as long as they are not breaking any company policies, I think that you don't have any say about what he does with her personal packages. How about you try to focus yourself on your work, and ignore the packages that he is receiving so that you don't get preoccupied about it.
I'm going to make a big deal about it at a manager.
You may be reprimanded by this manager and end up being humiliated in the end. I would suggest you review your company policies if it's really not allowed, but if it is not, then you should just ignore it as you are obsessing about something that shouldn't concern you.