Better than any other approach a free market helps to raise large groups of people out of poverty and promotes happiness through earned rewards.
During the recent Acton University I think an overarching theme of the talks and presentations was that those who believe in a free market economy must get better at making moral arguments.
May I recommend a couple books?
The Road to Freedom: How to Win the Fight for Free Enterprise by Arthur C. Brooks.
Defending the Free Market: The Moral Case for a Free Economy by Robert A. Sirico
Also, have a look at Poverty Cure.