At the core of the Republican philosophy is the constructionist interpretation of the Constitution. That is, Republicans are more likely to view the Constitution as meaning exactly what it says the way it is written, rather than lending itself to interpretation to fit the needs of the day.
Republicans are also generally opposed to more government; that is, they believe the government should do less and do it with less money. They generally oppose expansion of government beauracracy (sp?); more on this in a sec.
Republicans, at least in theory, oppose abortion. This obviously isn’t true of every Republican. Many are quite OK with abortion laws the way they are but would want to avoid any action that would expand or increase abortions. There are some, of course, who would prefer to see a Constitutional amendment banning abortion across the board. Ain’t gonna happen in my lifetime, but that’s another thread.
Most Republicans support the right to keep and bear arms and generally oppose most any gun control.
Republicans are big on law enforcement and big on the military and will generally favor increased military spending, tougher crime legislation, etc.
Republicans don’t like giving lots of money to public education and would like to make it easier for parents to put their kids into private schools.
Republicans generally oppose tax increases and are quite happy to support tax reductions, within reason. Republicans believe that the wealthy should have as much of their money as possible for this reason: the more money a wealthy person has to keep (instead of give to the government), that’s more money for him/her to put back into the economy; through investing, lending, purchasing, etc.
Republicans generally believe that the free market will offer a faster and better solution to a problem than the government will.
I said earlier that Republicans generally oppose more government. This isn’t exactly true. There is a group of Republicans, call them “Social Conservatives,” who would be quite happy to see more government, so long as that government regulates social issues. These are the people who would ask the government to censor movies, to ban certain violent video games, and to basically enforce social values. A pox on them. I say, let the free market bear it out. If parents stop buying violent video games for their kids, manufacturers will stop producing them. Economics 101.
I tried being a social conservative once, but I couldn’t do it. It was too inconsistent with my core Republican beliefs. For example, when the issue of riverboat casinos first came before Illinois voters in the early 90’s, social conservatives far and wide were vehemently opposed to it on moral grounds. At first, I opposed it, too. Not on moral grounds, but because the introduction of casino gambling to Illinois would give the Illinois General Assembly an excuse to write 20,000 pages of legislation in excruciating detail. Then I thought about it some more and decided that the prudent thing to do was to let the free market bear it out. If Illinois wasn’t ready for riverboat casinos, no one would patronize them and they would fizzle out. If Illinois was ready for riverboat casinos then hey: more jobs and more tourist revenue. Bring it on!
So that’s what this Republican believes, in a nutshell.