In response to your question about what the Republican party offers, I'd like to respond. First of all, the fact that you need to ask such a question parts out that there is much work to be done by the Republican party to explain what its message is.
Fundamentally, to my way of thinking, the big difference between the two parties is in regards to the role of the Federal Government. The Republican party generally wants to see a larger role by the Federal Government in regards to the military, and a smaller role in regards to pretty much everything else ("larger" and "smaller" here are in comparison to Democrats). The (Republican) idea is the more the Federal Government is involved, the worse for the Economy (by hurting Free Market Capitalism, because of higher taxes, regulations, etc.).
The Republican idea is one of a rising tide. For example, the poor are helped by a strong economy because then there is more money for everybody, including the poor.
Obviously this is a simplistic answer, by necessity, because of its shortness, but I think your answer is a good one, so have attempted a brief response. In short, (one thing) the Republican Party offers an alternative view to the role of the Federal Government, which (it believes) would result in a stronger economy, which will, in turn, benefit all citizens of the country.