One of my favourite libertarians was Harry Browne. He recently passed away, but his website remains, and it is a wealth of excellent libertarian thought. Browne consistantly wrote why the libertarian approaches to various social and economic problems are always the most effective and most consistent with the philosophy of liberty. He acknowledged that libertarian states would not make the world 100% perfect (what would?), but argued rather convincingly that a libertarians state is the best option when one considers the true ramifications of the other lesser alternatives.

Here are some of his best articles on various issues that I think you would enjoy reading:

What Liberals Can Learn from the Iraq War

Top 10 Government misconceptions

Terrorism

Iraq War

Free Market Problems

Anarchy vs Libertarianism

Gun Control

FCC & Censorship

Charity

Free Market vs Regulated Market (Computers vs Healthcare)

Enron & Corporate Scandals

Exporting Jobs

Public Education

Enviornmental Protection

Freedom & Responsibility

Gay Marriage

Healthcare

Social Security

Insider Trading & Martha Stuart

Taxes

A Gift for My Daughter (Great Read)

If you want a full index of all his articles, go here: http://www.harrybrowne.org/TopicalIndex.htm

If you're interested in learning about Libertarian thoughts and arguments, this ought to get your started.

If you want to refine your study more academically, I highly suggest reading from the thousands of available articles, audio books, and downloadable pdfs on Mises.org