There is no easy way to prevent the vertical scrollbar from showing up, short of disabling it completely, because you may simply have more content than can fit on screen.
If you wanted to disable the scrollbars completely you could use this:
body {
overflow: hidden;
}
However, that just means that content could go off the bottom of the screen and you wouldn't be able to scroll to it.
If you're displaying an image in the passage, you're better off just setting the max width of all img elements like this:
img {
max-width: 100%;
}
or you could set it for individual images like this:
<img src="images/Logo.png" style="max-width: 100%;">
(Note how the "max-width" is inside of a style parameter.)
If you wanted to, you could also set a "max-height" of say "200px" if you don't want them to be any taller than that.
Now, setting a background image is different, since it will be behind your text. For that you'd do something like this:
body {
background-image: url('images/Logo.png');
background-repeat: no-repeat;
background-attachment: fixed;
background-position: center;
background-size: cover;
overflow-y: scroll;
overflow-x: hidden;
}
That would make the logo fill the background behind the text, and it won't move if you move the scrollbar, just the text will move.
If you want that background image to only appear in passages that have a "logo" tag, then you could change "body" to "body.logo" (see the SugarCube documentation here for details).
Hope that helps! 
P.S. The "<style>" tag should not be in the stylesheet. Twine takes care of that automatically. Also, you can't use Twine or SugarCube code in your stylesheet. It should be pure CSS.