Background texture size in mobile phones?

I use the following C# code to attach background image to the scene to make 2D game menu:

 void OnGUI() {
     // display bg texture
     GUI.DrawTexture(new Rect(0, 0, Screen.width, Screen.height), 
                     backgroundTexture, ScaleMode.StretchToFill);
 }

The code is attached to Main Camera, with backgroundTexture mapped to a JPG.

Since mobile phones ( plan to support iOS & Android ) have different size & aspect ratio, what size should I make the background texture? Portrait orientation will be used.

p.s. I don't want to use StretchToFill, but I want the background image covering whole screen, while part of images (especially left & right) cropped by screen is acceptable.

Planned supported resolutions:

• Android: from 800x480 to 1920x1080

• iOS: from 640x960 to 640x1136 (no need to support iPad)