What kind of EM radiation best penetrate metals? My first bet would be infrared radiation, but I have no real idea.
If the answer depends on the particular metal, let's assume we are talking about aluminium.
 A: A way of answering this is in terms of the skin depth when the electromagnetic waves can be treated classically (i.e. in the IR-microwave-radiowave region).
The skin depth of a metal to electromagnetic waves of a certain frequency is given by $d = (2/\mu_r \mu_0 \sigma \omega)^{1/2}$, where $\sigma$ is the conductivity, $\mu_r$ the relative permeability and $\omega$ the angular frequency of the radiation.
From this point of view, for a given metal, then the lower the frequency, the larger the skin depth and the further the waves penetrate into the metal.
However, you would have to get down to ELF radiowaves for the skin depth of aluminium to reach as much as 1mm. Infrared radiation would be almost entirely reflected, any penetration would be limited to a few atoms.
The "skin depth" approach is appropriate for a classical treatment of electromagnetic waves. At high frequencies, a photon nature is more appropriate.
For optical radiation, I think you know the answer. A sheet of aluminium foil easily blocks visible light. UV transmission rises, but is still easily blocked by a micron of Aluminium.
Higher energy photons may be absorbed or scattered by the photoelectric effect, Compton scattering or Pair Production. Each of these processes has its own energy dependent cross-section which depends on the metal in question. For Aluminium you can consult the NIST tables, which give the mass attenuation coefficient as a function of energy. For Aluminium this has a minimum at around 0.02 cm$^2$/g for X-rays/Gamma-rays of energy of around 10 MeV. For a density of 2.7 g/cm$^3$, this gives an attenuation coefficient of 0.054 cm$^{-1}$ and hence a penetration depth of 18.5 cm.
So the answer is hard X-rays.
