Its really hard to pin down any static stereotypes between the two parties. Really, there are three types of republicans:
The religious right: comprised of southern baptists and their fundamentalist ilk. Spurning the idea of equality, they feel that America belongs only to them, and the rest of need to conform to their patriarchical authoritarian biblical ideals or leave. Led by nuts like Jerry Fallwell who break IRS rules and preach from the pulpit, you find them typically in the "bible belt" areas.
Laissez faire capitalists: These are the people who fantasize about getting Adam Smith drunk an taking advantage of his invisible hand. Though they do not often take positions on social issues, their economic position is clear, they want to government to have as little or no influence on the economy as possible.
Republican moderates: People who usually have a somewhat religious background, though still a far cry from the fundamentaists, and base many of their ideas on social policy from it. Economically speaking they may realize that some government regulation of the economy is necessary (to prevent things like the great depression, ensure safe working conditions, minimum wage etc) though often have a lot of scorn for social programs that they dont like (welfare, universalized health care, etc).
Of course these descriptions do not usually fit a person exactly, as they are usually some kind of amalgamation of the three.
Its kind of late so ill try and get to generalizations for democrats and some of the larger thrid parties tomorrow.