Spherical unwraps.

The U / Unwrap option uses the seams
You have not shown the texture you want to apply so we don’t know how it needs to be applied

For equirectangular textures you could use the Sphere Generated texture coordinates in place of UVs

For UV unwrapping a sphere to can start with a plane, map the texture to the plane and then bend the plane into a sphere http://blender.stackexchange.com/questions/24043/how-to-animate-morphing-a-rectangular-plane-into-a-sphere