You access the Live Paint selection tool options by double-clicking the tool in the Tools panel.

Select Fills

Selects the faces (the area within edges) of Live Paint groups.

Select Strokes

Selects the edges of Live Paint groups.

Highlight

Outlines the face or edge the cursor is currently over.

Color

Sets the color for the highlight. You can choose a color from the menu or click the paint swatch to specify a custom color.

Width

Specifies how thick to make the selection highlight.