I think the main Republican positions that define the party are easily available on the published party platform. I think most Americans will support those policy positions. Beyond that there are three core ideologies among those Republians in Congress.

Tea Party/Libertarian

Conservative Populism

NeoCon Conservatism

These three distinctive ideologies have only one thing in common, they reject the socialistic leanings of progressive liberalism. Only NeoCon conservatives like Cheney support the strong centralized Federal government that the Democrats generally favor.

Because of their "independence", Republicans in general have failed to have the kind of lockstep obedience of Democrats have enjoyed and say so. Nancy Pelosi through her control of campaign funding money has literally force members to end their careers on votes. So, if its concentration of power you fear... look to the Democrats, they truly are frightening. Fearing Republicans is like fearing a herd of cats will suddenly develop some discipline.