There are two broad forms of Anarchism, namely Anarcho-Capitalism and Anarcho-Communism/Anarcho-Syndicalism.
If you want to look into the first grouping, I would suggest the work of Stefan Molyneux (a self-described Anarchist), who runs "largest and most popular philosophy show on the web" (40+ million downloads of his podcasts, videos, and books) at http://board.freedomainradio.com/forums/ and https://www.youtube.com/user/stefbot. He also has a number of free books on his website (http://www.freedomainradio.com/FreeBooks.aspx), including two dealing specifically with the philosophy of Anarchism (Anarcho-Capitalism in his view).
There is a large group of his people on his forum, and with Mr. Molyneux being as professional, logical, and intelligent as he is, I suspect you could have a deep and respectful conversation with the members of the board should you be so inclined.
He also has an open-line show every Sunday (usually 1.5-2 hours long) which he takes all callers, indeed he has been looking to debate an anarcho-communist/anarcho-syndicalist but has had trouble finding one of any prominence who is willing to debate him in public. Feel free to call in (Skype is supported) if you wish to debate your views publicly. He also apparently devotes about a couple of hours a week on average to private discussions with those who wish to challenge his views, you might be able to get a private conversation with him if that is more your style.
I'm a little confused by the group description which refers to the goal of creating a "free market private property" society. I'm sorry, but that's NOT a goal of anarchism, as espoused by Pierre Proudhon.
In the past, I've met plenty of so-called "anarcho-capitalist libertarians", but to be quite clear, those people are not espousing anarchism. I hope this is a real anarchist group, and not a libertarian group.
I have really never understood how people can confuse anarchism with libertarianism. Corporations are absolutely tyrannical, and replacing the government with a "free-market private-property" society would simply reduce most of the population to feudal serfdom and abject poverty.
Ultimately, Proudhon was quite clear, "Property is theft!" If you don't agree, you aren't an anarchist. Of course, Proudhon was not saying that you do not have the right to own your own clothes, or a place to live. What he meant by "property" was the existing legal definition, based upon Roman law, via which an owner is free to do with his property as he pleases. In so doing, the owner robs the community of that property.
The notion of a "free market" system of "private property" is really the exact opposite of anarchism, as it rejects the basic notion that property belongs to the community, rather than to the individual.
-Adam Rinkleff