How does fuel efficiency depend on wing configuration?
The largest losses on a wing usually occur at the tip, where high pressure air flows around the end from the underside to the top side. This can be minimised by making the wing longer and thinner, or tapering it so the tip is smaller. You can also add winglets to reduce tip losses, but they're tricky to get right.

If you fly near the speed of sound, you get shockwaves that cause a lot of extra drag. You can slightly raise the point where they become a problem by sweeping the wing, and wing sweep also helps to reduce the drag when you are supersonic - but supersonic is never an efficient choice.

Drag is proportional to speed squared, so if you just want to fly for as long as possible, it's most efficient to fly slowly. However if you want to cover distance it's more efficient to fly really high where the air is thin. 

You can put all this together to get an airliner, with a long, thin, highly tapered wing (and winglets), flying so high that the air is only just dense enough to support it, and just below the speed that shockwaves cause extra drag.

You ask about wing position, and there is some interference drag where two surfaces meet. It is minimised by making the angle between the two surfaces as large as possible. Thus a mid-wing is slightly more efficient than other designs, but it's a relatively small effect. Wing position is usually determined by the undercarriage design and the pilot's field of view.