There is an all too neglected and ignored school of economics, and that is the Austrian School of Economics, lead by figures such as Carl Menger, Ludwig Von Mises, Hans Herman Hoppe and Murray Rothbard. I am of the opinion that every Libertarian should at least have some grasp on Austrian economics. Why? Well, to be frank, it is the only truly "laizzes-faire" school of economics in existance. The other basic options are classical economics, the Chicago School, Keynsian economics and supply-side.
The classical economists, while insightful, are not much help to us. The Keynsians are the epitome of socialism, so that's not a libertarian option. Supply-siders are mostly ignorant conservatives and the Chicago School of economics is a mixed school between the free market and socialism (with a disturbing undercurrent of Keynsianism on monetary policy). Furthermore, only Austrian economics is value-free and acts as an objective science, while most other economics is a matter of sweeping value judgements and econometrics.
The insights of the great Austrian economist Ludwig Von Mises are indeed very vital. Mises's ideas stretch way beyond what most people would consider the economic realm, but indeed it is all economic. Austrian economics is essentially the science of human action. "Human Action" was his work that really got things going. Mises provides a wonderful analysis of the fundamental question of human action by applying individualism and completely debunking collectivist constructs.
Only individuals choose, act and think - "society" is not an extra individual with a mind of its own, that chooses, acts and thinks as an individual would. People choose because they have made a subjective personal value judgement that the consequences of their action will achieve a particular desired end. This may seem simple and irrelevant, but it is incredibly relevant and applies to the entire economy and body of politics itself.
Most importantly, we must apply this truth to government itself. Government, through central planning, simply cannot calculate because it cannot read the minds of everyone. It cannot accurately predict people's personal value judgements, and therefore it cannot accurately predict the economy, no matter how many econometric charts and graphs are relied on. Government also cannot accurately determine the validity of someone's personal lifestyle choice that doesn't involve the use of force on others, and therefore it cannot make such choices for everyone through coerced exchanges or prohibitions without completely conflicting with people's personal value judgements and freedom of choice.
When government owns the means of production, it takes away one's ability to choose, act and think freely. It imposes arbitrary value judgements onto the multitude through the tool of uniformity, and therefore it is in conflict with human nature itself. No matter what government does, it cannot change the nature of human action. It cannot "cure" our fallability and limited sensory perception, and it can never make us all the same. And obviously, government is made up of human beings that are no less imperfect and limited then any other individual or group.
It should be quite evident that Austrian economics meshes perfectly with Libertarianism.