1. Cato-influenced (for lack of a better word). There is an orthodox reading of what "being libertarian" means, defined by the troika of free markets, non-interventionism, and civil liberties. It is based on individual rights but does not insist on anarchism. A ruling principle is that libertarians should not endorse state interventions. I read Palmer's book as belonging to this tradition, broadly speaking.
2. Rothbardian anarchism. Free-market protection agencies will replace government-as-we-know-it. War is evil and the problems of anarchy pale in comparison. David Friedman offered a more utilitarian-sounding version of this approach, shorn of Misesian influence.
3. Mises Institute nationalism. Gold standard, a priori reasoning, monetary apocalypse, and suspicious of immigration because maybe private landowners would not have let those people into their living rooms.
4. Jeff Friedman and Critical Review: Everything is up for grabs, let's be consequentialists and focus on the welfare state because that's where the action is. Marx is dead. The case for some version of libertarianism ultimately rests upon voter ignorance and, dare I say it, voter irrationality.
5. "Hayek libertarianism." All or most of the great libertarian thinkers are ultimately compatible with each other and we have a big tent of all sorts of classical liberal ideas. Hayek and Friedman are the chosen "public faces" of this approach. "There's a classical liberal tradition and classical liberal values and we can be fuzzy on a lot of other things."
Arnold Kling adds a substrand that he calls "civil societarianism" and which I quite like: "Collective institutions that are separate from government—good. Government—bad. Activities that can be sustained through profits or philanthropic donations can be presumed beneficial, from a utilitarian-ish perspective. Activities that require taxation are sometimes beneficial in theory, but public choice issues make them much less beneficial in practice."
I probably sit somewhere between the first and fourth categories: In general, we should oppose state intervention. At the same time, however, we ought to recognize that a certain amount of it is inevitable, and often not even terrible (if not exactly ideal), and thus strive to make sure that when government does act, it does so in a way that's effective and honest. Basically, it's about achieving the right balance between principle and pragmatism.
Of course, that's a tough balance to strike, and others will have different views on what's more satisfying, true, and effective. And that's a good thing! Competition between different ideas and approaches—even internal competition—is a necessity for keeping a political movement healthy.