At the outset, I commend churches that attempt to filter prospective missionaries. Perhaps the best way to do that is by being familiar with a couple of things: Their sending church and their supporting churches.
We see the sending church principle in Acts 13:3. Barnabas and Saul received favor from the church at Antioch. It was through that church that they were set apart to do missionary work. Naturally, a church will want to reproduce itself. In fact at the most basic level each disciple is to reproduce himself (according to Matt. 28:20 - "teaching them to observe all things...") with the end goal of Christ-likeness ("...whatsoever I have commanded you."). A disciple isn't a good one if he isn't discipling others. Churches ought to be concerned about a missionary's sending church because a missionary will represent and reproduce one's sending church.
As to supporting churches, we find in the N.T. a bit more of a sporadic nature (ex. Phil. 4:10-19, Rom. 15:22-33) in comparison to modern missions, however the Bible principles of giving with its broader applications including tithes, offerings, gifts, and alms certainly includes missions. A regular supporting church deserves among many things regular communication from their missionary. Also, there is strength in churches cooperating in missions work (ex. 1 Cor. 16:3,4; 2 Cor. 8:19).
Together the sending church and supporting churches working together is the N.T. pattern for doing missionary work and we can see in the Bible that a missionary is known by his sending church and supporting churches.