Armor is a shell of strong material encasing and protecting your tinfoil spacecraft. Unfortunately as a general rule, armor is quite massive, so it really cuts into your payload allowance.
Basically, the energy requirement to damage a surface is measured in joules/cm2. If you exceed that value, you do damage, otherwise you fail. Keep in mind that a Joule is the same thing as a watt-second.
There are three ways that weapon energy damages a surface: thermal kill, impulse kill, and drilling.
Thermal kill destroys a surface by superheating it. Impulse kill destroys a surface by thermal shock. In the calculations for the SDI, the amount to thermal kill a flimsy Soviet missile is about 1 to 10 kilojoules/cm2 (100 MJ/m2) deposited over a period of a second. The same energy deposited over a millionth of a second is required for an impulse kill. Since the laser beam tends to be meters wide, the beam energy is in the hundreds of megaJoules.
However, neither thermal kill nor impulse kill works very well with armor. So we use the third method: drilling. The amount of energy required to drill through an object is within a factor of 2 or so of the heat of vaporization of that object. There are also two other limits: the maximum aspect ratio of the hole is usually less than 50:1, and the actual drilling speed, for efficient drilling, is limited to about 1 meter per second (depending on the material).
Therefore, the best anti-laser armor will be that material with the highest vaporization energy for its mass. The best candidate is some form of carbon, at 29.6 kilojoules/gram. You do not want a form that is soft or easily powdered, or the vapor action under laser impact will blow out flakes of armor, allowing the laser to penetrate much faster. Steel has a higher vaporization energy, but it masses more as well.
Under laboratory conditions, if an armor layer was 5 g/cm2 of carbon, burning through a 1 cm2 (1.12 cm diameter) spot of armor would take about 148 kilojoules and 20 milliseconds. An AV:T laser cannon with 50 megaJoules could burn through 330 such armor layers in a few seconds, under laboratory conditions (i.e., enough layers to burn through the entire ship the long way).
However, under combat conditions there is no way one could focus the laser down that tiny and keep it on the same spot on the target ship for multiple seconds.
It would be better to use a beam focused down to a larger 10 cm2 spot (11.2 cm diameter). Granted the beam power required to penetrate jumps from 148 kilojoules to 15 megaJoules, but now if we have an uncertainty in the target's velocity of up to 5 meters per second it doesn't matter.
Of course, if price is no object, you can do better than carbon. Boron has a vaporization energy of 45.3 kilojoules/gram and is only slightly denser than carbon. Expensive, though.
In a 1984 paper on strategic missile defense, it suggested that your average ICBM would require about 10 kilojoules/cm2 to kill it. This would rise to 20 to 30 kilojoules/cm2 with ablative armor, and it would be tripled if the ICBM was spinning on its long axis since the laser couldn't dwell on the same spot 100% of the time.