Vertical layout

How do I set the plugin to display the icons stacked on top of one another instead of side by side? I’m currently using the shortcode to display it, but cannot see any parameters or any settings in WP for me to specify the layout.

By default, standard sharing bar shows icons side-by-side and floating sharing bar shows these on top of each other. Do you want to show icons on top of each other in standard sharing bar?

Also, how do I prevent the icons showing up by default on my page? Currently I have one bunch of icons positioned absolutely to the left, and another bunch of icons showing up by my post title… how do I disable these and display the icons *only* where I want them?

You can choose the page groups in Placement option to show sharing icons at. You can set position of standard sharing bar with respect to content in Position with respect to content option in Standard Interface section at sharing options page.
You can disable sharing on particular page/post as specified at following link:
http://support.heateor.com/how-can-i-disable-social-sharing-on-particular-pagepost/

Standard means the horizontal bar displayed at top and/or bottom of the page/post content. You need to tweak CSS to change icon alignment and save the CSS in Custom CSS option in Miscellaneous section at plugin options page.