For important things Keepass (which I sync in Onedrive). For casual things whatever the browser offers… or some random long password and password reset ._.
Ideally the logo should be something simple, because it gets displayed in many different places and usually pretty small. ~500x500px should be enough, and the main content should be inside a circle, because the corners are often not displayed.
A more detailed artwork is better for the bigger banner. Most communities seem to use something around 2000x1000px or so.