In the 1920s, there were three Republican presidents whose policies were largely similar to one another. We can look at their policies and goals in terms of both domestic and foreign policies.
In domestic politics, the main goal of the Republicans was to create a climate in which business could thrive. The Republicans were not interested in continuing to regulate business in the way that the progressive presidents before them had. Instead, they wanted to help businesses. Harding and Coolidge did this by reducing taxes and government spending and getting government out of the way. Hoover wanted government to do more to proactively help business. Their differences notwithstanding, they all wanted to help American private sector businesses.
In foreign policy, the main goal was to avert the possibility of another world war. The US did this through such things as the Washington Naval Conference treaties that were meant to prevent arms races and the Kellogg-Briand Pact, which outlawed war. The US also tried to help Germany to pay the reparations forced on it by the Treaty of Versailles. However, this was meant as much to bolster the international economy as to prevent war.