I noticed that plane which is constructed in unity has many faces/vertices (or how they are called),
is there a way to make the vert count smaller? and still be able to drag and drop a texture on it?
cause, for now, - correct me if I'm wrong - but it seems to me that it's less costly to use a flattened cube than a plane.
There is also a simple plane available on the asset store.
You can just do GameObject → Create Other → Quad in Unity 4.2 or later.
Unless this has changed in Unity 3, the only built-in rectangle primitive that's available is subdivided (as in your image). However, you can create a simple 'quad' model and import it, or create an appropriate mesh procedurally. (I believe there's actually a script somewhere on the wiki that creates a plane at a specified subdivision level and saves it as a mesh asset.)