In aiming for early wins, and in the longer term, it is important to know what you are trying to achieve. Of course, you cannot decide this in a vacuum. Quite apart from any consequences to customers or colleagues, it is vital that you and your boss are of the same mind. The best way to ensure this is to talk to them.
This is also the time to deal with any differences in style. If, for example, you take a team approach and your boss is more hierarchical, they may mark you down on stylistic issues. This is not deliberate, but more that the potential results will be hidden from them because you are not doing the job the way they would do it. It is therefore important to point out these differences, and to negotiate enough time to start to deliver tangible results.
The worst thing that you can do with your boss is to overpromise and underdeliver. You therefore need to agree some realistic goals, and enough time to deliver them. This presupposes that you have negotiated time to make a proper assessment of what needs to be done.