It is difficult to provide a comprehensive answer to this question as Republicans have a wide range of beliefs and priorities. However, based on the search results, here are some of the things that Republicans want:

• A more conservative House Speaker: According to a recent poll, about half of Republicans want the next House Speaker to be "more conservative" than the previous Speaker, Kevin McCarthy.

• Spending cuts: House Republicans have proposed cutting spending on a variety of programs, including education grants for low-income schools, Medicaid, and food assistance through the Supplemental Nutrition Assistance Program (SNAP) . They argue that these cuts are necessary for fiscal responsibility, but critics argue that they would hurt hard-working families and vulnerable populations.

• Conservative policies: Some Republicans are pushing for policies such as a "mental competency" test for candidates over 75, raising the voting age, and imposing the death penalty for drug offenders.

• Sticking to principles: Many Republicans want their elected officials to stick to their principles, even if it means not compromising to get things done.

• Lower taxes: Republicans generally favor lower taxes, and many of their budget proposals have included tax cuts for the wealthy and corporations.

Its worth noting that these are just a few examples, and there are many other issues and priorities that Republicans care about. Additionally, not all Republicans agree on every issue, and there is often debate and disagreement within the party.