To answer your question about which category under 501(c) the Tea Party should have applied for; the answer is none of them. By the wording of the original law, political organizations should not be getting any 501(c) designations.
I'm sorry, but this is beside the point. If there are going to be 501(c)(4)s, the IRS has to judge them fairly, and they weren't. Maybe you think the AARP, the NRA, the League of Conservation Voters, the Planned Parenthood Action Fund, the National Wildlife Federation Action Fund, and all the rest should be taxed like for-profit corporations, but under the interpretation of the law that has existed for decades, they aren't. And if you are going to change that, don't change it for one political view, and not for the others.