Your question has quite a few different components. Pure democracy is based strictly on the will of the people. We have a representative democracy in which the people elect representatives who should "represent" the views and interests of those who elect them. Our founders set our government up to be a republic. They also knew it would be difficult to maintain as such but they had great belief that it would be possible
Economically, there are essentially two competing ideas or systems, socialism and capitalism. Each of these has variations and extremes.
In capitalistic societies individuals and businesses compete in a free and open marketplace with limited government control. This can lead to development of an oligarchy
Socialist societies are a government based solution in which the marketplace is centralized. Everyone contributes to the society and gets equal benefit. The idea being that there should be disparity between rich and poor. Everyone is "equal."
Both economic systems have problems. Capitalist societies often have large gaps between rich and poor. Those who are successful become more successful and it can become very difficult for middle and lower classes to have the same opportunities as those of higher classes.
Socialist societies on the other hand also have great challenges. When people are not rewarded according to their effort they tend not to work as hard. Quality of services and products declines. Although the idea is that everyone will be equal in socialistic societies, those who have high governmental positions often become "more equal" than those in the working class. They give themselves benefits which are not available to workers.
Neither of these systems is perfect. In the United States we have based or economy on capitalistic principles. This type of system can lead to oligarchy like conditions where the rich become richer and the poor don’t have any opportunity to increase their social standing. We do however have a significant amount of government control and regulation which has both positive and negative effects. Many regulations are established with the intent of protecting middle and lower class workers. Many of these regulations are necessary in most people’s opinions in order to protect average working class Americans. Some of these regulations however have unintended consequences which make it difficult for businesses to be successful. Many also affect small business and take away opportunities from those who might be striving to move from to lower/middle class to a higher class by starting businesses.
The great debate in our country right now is about these very issues. Some say that government should be more involved in giving opportunities to those in the lower/middle class. Other say that government involvement has caused many of the economic problems we are facing. Some say that the solution is to tax the rich in order to help and those who are less fortunate. Their argument is that this will equal the playing field and create a country where there is opportunity for everyone. Others say that this will discourage the wealthy from starting new businesses, providing jobs, creating and inventing products and technology etc.
These arguments are essentially about which direction our country wants to go on the socialism/capitalism spectrum.
In general, democrats want to see an America with more equality between classes. They want to accomplish this by enacting fairness. Higher taxes on the rich, regulations to prevent business from exploiting average Americans, more government intervention to help the poor such as welfare programs, healthcare, aide for home buyers, food stamps, more free student aide, higher minimum wage etc. These are all very noble ideals but sometimes they have unintended consequences. They may move us closer to socialistic style government. They may take away people’s ambition to work hard and create and innovate.
Republicans believe in the reward based on merit and hard work. They feel that government should be very limited in the help that it offers to individuals. In general, they believe in lower taxes and allowing people to keep more of their own money in the hopes that they will use it to create opportunities for themselves and others. They tend to believe in the philosophy “If you give a man a fish you feed him for a day. If you teach a man to fish you feed him for a lifetime.” They believe that in a capitalistic society there are winners and losers. The winners are rewarded for their hard work. The hope is that everyone will be motivated to work hard and make their own way and there will be much less need for government to care for the less fortunate. “The rising tide lifts all boats.” This also has unintended consequences. It assumes that everyone has an equal opportunity to pursue success which is not always true. Being born into difficult circumstances often makes it nearly impossible for lower class individuals to climb the social ladder. Those with money are much more likely to be successful than those without. There will always be a gap between rich and poor that will be difficult to bridge.
I hope this gives some good information. As I have said previously, neither system is perfect. It is important to have balance and the truth usually lies somewhere in the middle.