I need to marry the classical model of the colliding electrons and atoms of the medium with the Quantum principles involving the excitation of charges to higher energy bands and emission of photons.
My answer to this question explains something about the concept of the conduction band.
Think of it this way. In all the filled shells (including shells that will be filled by to atoms joining into a lattice or a molecule e.g.), all slots are taken. There are no more spots for electrons to move to - no vacancies. Therefor, no electrons can move (because of the exclusion principle, there can never be to electrons at the same exact state). These are called the valence bands.
The unfilled shells make up the energy states in the conduction band. It is called the conduction band because it is not full, so electrons can move from one state to an empty one. This gives freedom of movement within the band and throughout the same energy state stretching over many atoms in the lattice. The Wave function of the free electrons spreads over many atoms - they are not "bound" to a specific atom anymore. This is a conductor.
For a very little force (that is, a very little electric field) the electrons can be pushed from one energy state to another within the band. When this electric field is applied the charges will move (a current will flow).
Especially in semiconductors, more electrons can be moved up to the conduction band be being excited from addition of energy (light, heat etc.). Here conductivity can rise from higher temperature (to some extend). In usual metallic conductors, their conductivity will usually decrease with temperature, since more collisions will take place and less freedom (essentially less energy states to move to because of many already taken slots) is the result.
Also, a second question is what causes the electric field in the conductor to be practically zero (compared to that in the resistor) in a non - electrostatic model (i.e., when there is a current).
The electric field is not zero in a conductor. If it was, current would stop flowing, unless it was a superconductor. The electric field in a circuit is caused by e.g. a battery. This provides a potential difference from one end of circuit to another (over all the circuit components). A potential difference is essentially a willingness of electrons to move from higher to less potential energy. This is the case since charges set up an electric field throughout that will drag them along.
In a resistor this electric field (seen as a potential difference over it) is still present. It is just harder for the charges to move through the material.