There is no stated purpose of the house church, nor do we think there needs to be. God has given us the purpose of life in the great commandment and the great commission.
Great Commandment: "You shall love the Lord your God with all your heart and with all your soul and with all your mind. This is the great and first commandment. And a second is like it: You shall love your neighbor as yourself. On these two commandments depend all the Law and the Prophets." (Matthew 22:37-40)
Great Commission: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age." (Matthew 28:19-20)
The purpose of the church (the body of Jesus Christ) is to make his name great among the nations. (Video: Biblical Basis for Missions) We see the house church model as the most biblical and practical way to make that happen.
Does each house church have its own mission statement?
There is no need for each church to have its own mission statement. We have already been given the mission (referenced above in the Great Commission). "The Great Commission is still the mission statement of the Church." (Dallas Willard)
What does success look like for the house church?
When people are eagerly seeking God and His word (Great Commandment), demonstrating genuine and vibrant love to those around them (Golden Rule: Matthew 22:39), and making disciples of Jesus Christ (Great Commission), this is success. Success is not more people or more churches. It is easy to attract a crowd! However, that is not what Jesus asked for. Jesus regularly sent away the crowds when he saw that they were not interested in sincere devotion to him (see John 6). A house church has the best built-in system of helping people know and obey God's word. Success is obedience to Jesus!