First, as to the local/universal church argument. I believe that I believe that the church has its present, visible manifestation in the institution of the local church. And, I believe that this local church is the main emphasis of the New Testament and is the church through which God does His earthly work in this age.
Yet, I also believe that there is a spiritual body of believers. This is the body of Christ to which all believers belong. In the sense that all believers are "in Christ" and members of His body, flesh, and bones (Ephesians 5:30), in that sense we are in the body of Christ. This body of all believers is ultimately the church for which Christ died on the cross (Ephesians 5:25).
However, this body of all believers is not the body through which God does His work on earth today. It is incomplete since some have not yet been saved. It is scattered with some on earth and others in heaven. It has not yet met for its first church service. It is indeed the church in prospect and will in the future be the body through which God does His work. Though it is today a spiritual reality, it is not yet in operation practically. Knowledge of its existence provides a wonderful inner blessing but it cannot be used in a plan for world-evangelism--that is the job of the local church--the church of this age.
Now, as to what constitutes a New Testament church. It is a body of baptized believers organized for the purpose of assembling as a church, ministering to each other, worshipping God, and reaching out to a lost world. Matthew 18:20 where two or three meet together in His name is only the seed doctrine for the church. It is not a full definition. That must be developed from many scriptures.
Ultimately, the church is the people. We see this in Acts 14:27 where Paul comes to Antioch and the church is gathered together so that he might report to them. But a church must also be scripturally organized as a church. A casual meeting of believers is not a church. A church is tied to a location throughout the New Testament. I believe it is made up of baptized believers (Acts 2:47). It is to be ruled over by a pastor (1 Timothy 3:4-5) though it certainly does not cease to be a church when it is between pastors.