Voter ID One vote per citizen, no votes for non-citizens. It's not unreasonable to prove you are who you say you are. People have to do that all the time already in other contexts. It's not unreasonable. People need to trust the integrity of elections or the whole system breaks down.
Gay Marriage Most heterosexuals have civil unions (get married at the courthouse, not in church/temple/mosque), gays can have them too. They cannot force religious institutions to perform ceremonies.
Abortion If you want to use birth control, use it at the outset. If the child could live on its own outside the womb, you cannot kill it, that's murder. If the woman wants it removed, she needs to find someone who will take care of it first (I'm sure there are plenty of adoption agencies that will gladly take it, especially the strident anti-abortion ones: put up or shut up!). If the fetus could not survive on its own outside the womb, I'm reserving judgment for now. The tricky part is how the whole situation is affected by technology.
Gun Safety Treat them just like cars. Universal education at a young age in how to use them and care for them properly. You must get a license and a title and carry liability insurance. If you sell it then you re-file the title in the new owner's name.
Health Care The states should be in charge; so many elements are based on local conditions that very greatly from one state to another. Allow an option to purchase a standard catastrophe only policy. The federal government should not be mandating anything in this regard. The federal government should not even be paying for Medicare or Medicaid directly either, too much fraud and waste. Every week we read about another arrest made of doctors defrauding the system, ordering tests that were never performed, etc. Give eligible people a credit based on some formula and they then use that credit toward the purchase of an insurance policy from a private vendor. Educate people on the role that The National Association of Insurance Commissioners plays in coordinating states' insurance laws so that we all feel more comfortable leaving the states solely in charge. States really do coordinate closely on most insurance regulations and there is already tremendous uniformity in most situations about most kinds of insurance; yet there is still flexibility (FL has hurricane-specific rules that don't apply in ND; CA has earthquake-specific rules that don't apply in RI).
Education Give eligible people a credit based on some formula and they then use that credit toward tuition. Make "public" schools compete with alternatives. We have wasted too many inner-city futures already to allow the status quo to continue, this shameful waste is definitely the defining civil rights issue of the day right now. At the same time, we have a basic set of standards that everyone targets as a minimum goal for learning.
Remove the Department of Education from the federal government and turn it into the National Association of State Educators or some such title. The states can manage a coordinated approach with local variation just fine.
Foreign Policy The world economy is intertwined and interdependent. We cannot ignore what happens in other countries. Rather than approach each situation on a case-by-case basis, develop a set of consistent principles to apply in every case. Example: free trade. Tariffs are bad. Subsidies in the long run are not effective.
We also have to have a hard-headed sense of realism. There are some really bad people, evil people, in the world, who would gladly kill us if they could. We cannot let them, and we must stop them.
Monetary policy Maintain a stable price level. Period. No other responsibility for the Federal Reserve.
"Entitlements" There should not be any. It is not the government's business to legislate morality. At the same time, society has a responsibility to take care of everyone who needs help. It is the direct involvement of giver and receiver in a social compact that we really should be emphasizing. By passing off this responsibility to government, we do everyone a disservice.
No one has a "right" to any specific tangible physical good, except private property rights in general are essential (exception, apparently, is gun ownership. Go figure): otherwise, if we run into a time of scarcity, society tears itself apart (look at the Colorado River: various entities now have "rights" to more water from the Colorado River than exist). People "should" share during times of abundance and sacrifice during times of scarcity, of course, but not by government mandate.
Taxes Government currently spends way too much money for far too little in return. If government spent a lot less, then we'd look at the economic impact of taxes on human activity as the most important consideration, instead of scrounging for more and more revenue all the time instead.
Free Speech Rights If you want to restrict corporate speech, you restrict union speech rights too. If you allow union speech rights, you allow corporate speech rights too.
Governmental organization 15 federal cabinet departments is absurd. Streamline and reorganize into essential functions, six is probably adequate: War/Defense; State/Diplomacy; Legal Department; Treasury/Accounting; IT/HR; Resource/Land Management.