All good stuff so far. I'll just add two things I didn't see:
Manage your own to-do list effectively and follow through on what you promise to do. In other words, manage yourself so your manager doesn't have to, and say what you are going to do and do what you said. This seems so obvious, but I have seen so many people over-commit (with the best of intentions) and not deliver.
Take advantage of your honeymoon period to ask stupid questions that aren't really stupid. You have a period of time to be the "I don't know how this works" guy without it being negative. In the process of asking these questions, you are likely to find out that a bunch of other people don't know the answers either, but then the information is out there for everyone.
Re: The New Job
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That first one has a caveat though - make sure to let your manager manage you when they want to. Don't become so intent on being independant that you do what you want to do instead of what you are being told to do. Your might be able to manage your own to do list, but your boss is still in charge :)
My cow-orkers were talking in punctuation the other day. What disturbed me most was that I understood it.