When I was about 8 years old I watched Ayn Rand on Donahue with my father. I was too young to fully understand the things she was saying. I remember having a deep sense of respect, as the things she was saying were completely different from the things I had heard adults around me saying at the time, and they seemed to quell a lot of the existential pain and confusion I felt from a lot of those things adults would say. (I couldn't define it then as such, but subsequently have.) I just remember wondering why the people in the audience were hissing at her when she was championing their rights as individuals.
When I was 13 years old I found a copy of the The Fountainhead on a trash can in San Diego. I was finally capable of studying her and of actually understanding the things she was explaining in her allegories. I have never found a philosopher, before or since, that hadn't contradicted themselves and that could logically back up her philosophical conclusions, as she has.
http://www.logicalfallacies.info/ That's just one site, there is a lot more research available but this is the best place to start.
After I had read all of her ficiton and most of her nonfiction I starting reading a lot of the Ojectivist essays and websites. I realized I was in a real danger of completely adopting everything someone said simply because they deemed themselves Ojectivists. I was 16, and decided I needed to study the competition, In a lot of ways, I changed some of my moral premises to try to live some things out to their logical (though in all cases illogical) ends.
I was always faced with moral ambiguities, not to mention the anxiety that comes from living life as an animal would, in a lot of cases. I am not only an animal; I am a rational, conscious human being. I live on planet Earth, and I do believe that there is a correct way to live as such.
Some reasons I've noticed that a lot of people misinterprete Rand is because 1) they haven't taken the time to actually understand her philosophy (by far the largest), 2) they don't understand the entire thing (the moral and ethical misconcetpions that we have are far more wide spread and indoctrinated then most can conceive), 3) they do not want to live rationally and freely. Though there may be other reasons I haven't come across any as of yet, that are valid. Can you?
As far as her being a "political paranoiac", have you heard about the Patriot Act? And capitalism, in my research of economic systems, has produced the best standard of living--from rich cats to minimum wage workers--for its human components, then any other economic system in history. Walk around with a camera in the third world and it won't be two minutes before you have someone asking you to take them to the US. Free market trade is the only ethical style of commerce.
To understand Rand, read her allegorical novels, then read her nonfiction. It's a beautiful way to learn a philosophy (kudos Rand) and it will allow you to watch her conclusions work in human context. Notice, not in some heavenly or fallacious context, but in reality.