If you want to select half the vertices to delete them before the mirror modifier, just select the midline of vertices on the front and back and hide them. Then from front orthographic view, its very easy to box select one side and delete them. Unhide the hidden vertices, go to object mode and add the mirror modifier.
Yes llizyorick ,
and quick selection methods are extremely useful! You could also after hiding the midline, use L to select one half.
And if you're lazy (or practicall) and care to enable the Auto Mirror Addon that comes with Blender, you can do all that (removing half the Mesh and adding a Mirror Modifier) with just one click:
