I'm not American, but from an outside perspective, having in mind the many American opinions I've read, I'd say the most interesting choice would be the (a?) libertarian party.
I've often talked with Americans who are fiscally conservative yet socially progressive, so all they can do is ignoring one preference when voting for "the lesser evil". And some even feel they have no choice at all, being trapped between statist liberal supporters of a "nanny state" and authoritarian big-government conservative supporters of a "daddy state".
So my guess is that a truly libertarian party, especially when it's sufficiently moderate and less focused on ideological purity, has the potential of getting the support of a large number of Americans. More certainly than, say, the Green Party.
But then, third parties will not likely play a role as long as the plurality-based electoral system is not replaced by another, such as proportional representation or so.