How academic do you want? Or are you looking for a more popularized history?

If academic, start with Claude Bowers' The Party Battle of the Jackson Period which denote the Whigs and Democrats battles of the 1830's, and the eventual demise of the Whigs.

Then, jump to The origins of the Republican Party by William Gienapp. This will go into extreme detail on the rise of the Republican party from sectional to national. Beware, it is a detailed read, but well researched.

There are any number of Lincoln based books/biographies that will detail the Republican rise to power, but of interest to me is the changing mood of the republicans as there were IN power. William Gillette's Retreat from Reconstruction is an excellent source to cover this timeframe.

A Fierce Discontent by Michael McGerr is a good quick one to cover Progressive politics from 1890-1920, which covers TR and the Bull Moose party. If you liked Claude Bowers writing, he also had one on the Progressive movement, focusing on Senator Albert Beveridge of Indiana, titled Beveridge and the Progressive Era.

After that, I'd go with presidential biographies to get the gist of the party lines, but that gives only a partial picture. After the 1920's I am not really an expert.