Don't know about an ideal world for the GOP.
Mine would be where people are responsible for their own selves.
The gov't doesn't tell them what to do, though there are laws of what you "cannot" do to others.
The gov't exists to protect the borders and the citizens from invasion.
Schools (supported by the community, if your community doesn't want to support the children, then it is left to the parents to see to the education, not the "state") teach children the academics (not social engineering), if children do not want to learn, they are told to leave (to allow those that want to learn to be able to learn without rude distractions)
Universities are supported by larger communities (county or state) or are private (no federal dollars for education).
Charity is used to provide assistance to people that need help at a community level. If that community can support additional aid, the "community" can set up the means or taxes to do this. (The system is not abused by people that are "stealing" from the taxpayers)
The Bill of Rights would be posted at every police station, every courthouse and every public building so that the citizens and the gov't workers would be reminded there is a higher power than gov't.
The fourteenth amendment would be gone. "Men" is the proper term for large groups of people, male and female, any race. There would be no "anchor babies". There would be no excuse for the gov't to overstep the Constitution.
EVERYONE would pay taxes at a set percentage (like 10%). If you could not pay taxes, another could pay them for you, or you would do community service instead.
Holidays would be federal only for Thanksgiving (established at the founding of the early settlement), Forth of July, and President's Day. Other holidays would be "floating holidays" (decided by the individual), so that people could take off for their own religious days. There would be no Christmas holiday for congress and Presidents (unless they used their floaters).
In short, I cannot think of a better system than the founders of this country established two hundred and thirty seven years ago. For the life of me, I cannot understand why so many on the left want to take us away from the gov't that established the most prosperous country in the history of the world with the highest standard of living to a country where there is less freedom, more tax burden, more gov't, and a lower standard of living.