"And they move at 186,000 miles per second, knocking on a bit."
As ChuckFickens said, it's not that the electrons move at that speed. Under Einstein's Relativity, it is technically impossible for an object with mass to achieve light speed. It is actually the electric FIELD that travels down the wire at 186,000 miles/second.
I could very well be wrong as it has been a while, but I am pretty sure the atoms do NOT travel from atom to atom. They travel in the spaces between the atoms - a material that can conduct electricity has lots of electrons loosely bound to its nucleus so under certain conditions (like an electric field) they can move freely and travel about in the spaces between atoms. This is a classical description, so there could very well be a different quantum description.
As for resistance, they way it was kind of explained to me is,for a given voltage over a wire, the electrical field will try and push a certain number of electrons each second along the wire, regardless of how thick the wire is. An analogy would be trying to push a given number of women (i.e. electrons) per second along a corridor. The corridor has already got a number of men per sq metre standing around in it doing nothing (i.e. atoms). If the corridor is narrow then it it is difficult for the women to get past without jostling against the men and other women, creating heat. If the corridor is very wide then it is much easier for the same amount of women to get though without jostling, therefore less heat.