All of the above and yet at same time, none of them entirely.
Perhaps the best for me would be a fiscally conservative, anti-populist New Rightist, if such is possible. I consider myself an inheritor of Burke and Hamilton, yet with the lessons of hindsight about the negative impacts of gov't going to far during various periods of the 20th century and today. But in spite of that, I do think there is a limited role for Gov't to play. At the same time, I hate the idea of the gov't actively deciding specific winners and losers in most instances so that is more Libertarian then a corporate rightist. I also think that while a strong federal gov't is necessary just like Hamilton and Burke did for the purposes of security and stability, but that it has also been taken too far in modern times and that there is a place for states rights as a means of preserving an important check on federal power.
As for the history, "The Corporate Right" would have moved towards or became the Libertarian right to an extent in the 1930's. Prior to that, they saw Gov't largely as a tool for their own benefit through stability, trade protection and currency regulation. When it was taken further than that, not for their benefit, but at their expense they began to embrace a more anti-gov't posture, one that just a few decades prior they would have scorned. Stability was a forgone conclusion with a century+ long established gov't system and laws, trade protection was starting to hurt them more then help and the Fed had been created. Their desires realized, they had no need to maintain an advocacy for stronger gov't. They would still support policies that benefit them, but would oppose anything that didn't. A nuance which continues to this day.
New Right is merely a combination of several of the others, most notably the Religious Right and the Corporate/Libertarian Right. In 2000's, the former really got the upper hand on the latter. However, the rise of the Tea Party, and the nomination of Mittens provides the possibly of restoring the blance between them atleast to the extent that such existed in the 1990's. Had the opposite occured, the risk would have been a decline of that fiscal conservative/libertarian quadrant's base or potential base to the point that reversal became impossible and Conservatism ended up being defined by Huckabee. Scary thought.
Edit: Yes, I do realize that Corporate Right, Libertarian Right and Fiscally Conservative aren't exactly the same thing. They do overlap considerably, espeically when talking about their base, which is usually middle, upper middle and upper class income levels and more highly educated people. The constant overtures to the Social Conservatism and let downs for these three groups since the 1990's, means that this demographic has been leaving for the Democrats. Without them in primaries, poorer, less educated populists will gain more influence in the primaries creating a self-fulling prophecy of socially conservative, big gov't populism.
Republicans, is this pretty objective? Are these good categorizations for Republican factions?
It's a good attempt. Some of the descriptions are not how people would describe themselves (ex. I don't think Eisenhower would choose to call himself "corporate"). I think there also needs to be a place for people who are conservative in the sense of traditionalist, but not movement conservatives, who focus on small business and localism, and social conservatism without much sectarian overtones - "Main Street Right", perhaps. There's some overlap with the Old Right, but these are people whose views are less strident than the descritpion suggests, and may be inheritors of Burke as much as Jefferson.
The thing to consider is, these are strands held in common as often as they are factions, with the greatest number drawing on more than one and not identifying with any one exclusively.
I agree completely.