As a user I'd like to have:
window mode + free resize or set of multiple good resolutions (regard something like titlebar height, taskbars or menubars)
fullscreen + monitor selection (name of monitor + resolution for clear selection)
windowed fullscreen mode (window without borders) + monitor selection or free resize + window moving (for support of having a window stretched over multiple screens)
As a game developer I'd like to not think about it and just have a setting for this.
As an engine developer I'd like to have an abstraction layer of monitors, screen layouts (which screen is next to which one) and user areas (substraction of window borders and taskbars from screen area).
There are different choices for the window to launch. Best case: it is stored so on next start it is exactly at the same location (if the same screen layout is used). For first launch: where is the taskbar, on which screen is the mouse, where is the parent window (steam).