XNA
Local
External
Background
A good size to make the background is 1280x720 (720p size), and let is scale.
Or maybe make multiple images of the right sizes.
Texture2D backgroundTexture;
Rectangle screenSize;
// LoadContent()
backgroundTexture = content.Load<Texture2D>("resourceId");
screenSize = new Rectangle(0, 0,
graphics.GraphicsDevice.DisplayMode.Width,
graphics.GraphicsDevice.DisplayMode.Height);
// or maybe...
screenSize = new Rectangle(0, 0, graphics.PreferredBackBufferWidth, graphics.PreferredBackBufferHeight);
// Draw():
spriteBatch.Begin();
spriteBatch.Draw(backgroundTexture, screenSize, Color.White);
spriteBatch.End();