Welcome to the Mises Forum!
Definitely check out The Ultimate Beginner meta-thread for a comprehensive collection of relevant links and threads. I think you’ll find it really useful. (Also be sure to check out the welcome link there for forum tips and how-to’s)
You pose an interesting task. I suppose such a list would have been quite useful for me at some early point…although the problem with such lists is that they generally get a few things inaccurate. At the very least there are people who subscribe to one or more of the terms and yet don’t identify with the common understanding of the word.
“conservatism” and “liberalism” are two of the hardest, because they are so widely used today, and yet have meant so many different things through history.
I haven’t read through this whole thing, but at a preliminary glance, it seems a lot more accurate than most…and definitely more than one would expect it to be. I think it’s a decent starting point.
Conservative vs. Liberal Beliefs
Socialism generally refers to a level of State control of an economy. Where exactly that level is, (i.e. when exactly you have “socialism”) is a matter of pretty contentious debate.
I describe capitalism here.
republic I tend to think of as “rule of law”…Mises describes speaks on this here.
democracy I would say is majority rule as well. The Founding Fathers had a few things to say on that.
libertarianism…that’s a big one. Especially within the community of people who consider themselves libertarians, there is a really wide range of definitions…at least in the details. The general principles are that of non-aggression and private property. See the section “libertarianism” in the beginner meta-thread.
anarchy is pretty well defined by the dictionary the way you put it. But others believe it to inherently mean many other things…the most common of which is “chaos”.
Again, welcome!