I didn't read the "(a purely classical number, but most won't have a clue)" as being part of the question, but rather as commentary about people answering the question. Also "how fast do electrons move" does really suggest the velocity of an electron and not the net average velocity...anyway, calculating drift velocity is easy. From the current and the charge of an electron, calculate how many electrons are passing through the wire per second. Then calculate the number of electrons in the wire from the material properties. The answer is the ratio between these two, multiplied by the length of the wire. Since this contains many numbers that most people (even physicists) don't know off the top of their head (density & weight of copper, avogadro's number, electron charge) this is a bit hard to guesstimate within an order of magnitude without looking things up, but it will be a small number of meters per second.