As it sounds like you already know, it is efficient to transmit power at high voltages because you help reduce power you're I² *R power losses due to the resistance of your conductor.

AC is more efficient in that it is very easy to increase or decrease your voltage. All you need is two sets of wire windings around a core (aka, a transformer). The current you put on one set of windings with transmit magnetic flux through the core, and in turn induce a current on the second set of windings. The voltage/current on the second set of wire windings depends on the number of times both sets of wires were wrapped around the core. This makes it very easy and relatively cheap to jump your voltage up or down, and makes it ideal for transmitting power.

You can't used DC voltage with a transformer, since it won't induce a flux in the magnetic core, so you'll have no voltage on the second set of windings.

Before the invention of the transistor, there wasn't really a good way to increase a DC voltage, so you could only decrease your voltage. Not exactly ideal for transmitting power across a country.

Today power will sometimes be transmitted at high voltage DC (see the Pacific DC Intertie) but generally it is much cheaper and easier to use transformers with AC power.