New Testament -- Acts 17: 

22  Then Paul stood in the midst of Mars' hill, and said, Ye men of Athens, I perceive that in all things ye are too superstitious. 

23  For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD.

Whom therefore ye ignorantly worship, him declare I unto you. 

24  God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands; 

25  Neither is worshipped with men's hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things; 

26  And hath made of one blood all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the bounds of their habitation; 

27  That they should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us: 

28  For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring. 

29  Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man's device. 

30  And the times of this ignorance God winked at; but now commandeth all men every where to repent: 

31  Because he hath appointed a day, in the which he will judge the world in righteousness by that man whom he hath ordained; whereof he hath given assurance unto all men, in that he hath raised him from the dead. 

32  And when they heard of the resurrection of the dead, some mocked: and others said, We will hear thee again of this matter. 

33  So Paul departed from among them. 

34  Howbeit certain men clave unto him, and believed: among the which was Dionysius the Areopagite, and a woman named Damaris, and others with them. 

It is true that only a few stuck around to talk with Paul further.  But, that's more than we get preaching the Bible to "unchurched" folks.  Undoubtedly, Paul, moved on soon to introduce them to the Scriptures. 

Let us further look at the New Testament -- Romans 1.  This is the letter by the Apostle Paul to the new Christian Church at Rome. 

I emphatically say that, here alone, in all the New Testament, is the Gospel (meaning "good news") set forth in fairly systematically manner.  Aspects of the Gospel are touched upon throughout the New Testament, but only here, do we find a formal presentation, though not exhaustively so -- there are some details missing here, and found elsewhere.

Romans 1:15-25: 

15 So, as much as in me is, I am ready to preach the gospel to you that are at Rome also. 16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.

17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith. 18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness;

19 Because that which may be known of God is manifest in them; for God hath shewed it unto them. 20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:

21 Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. 22 Professing themselves to be wise, they became fools, 23 And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things.

24 Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves: 25 Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen.

Again, emphatically, I say, that the Gospel presentation correctly starts with what we call, NATURE, NOT with SCRIPTURE (the Bible!)  God's initial, and primary, interface with most people is the physical world, NOT, the Bible! 

We should take an important lesson from this.  As is clear in verses 18-20, mankind's knowledge of and realization of God existence, is absolutely certain from God's created physical world.  Further, God's judgment has been ongoing due to mankind's dislike and disregard of him, and their failure to give God glory and thanksgiving for all he has made, and provided for them.

Thus, God's physical creation should be our evangelical starting point, especially for unchurched folks.  This passage makes clear that all mankind is on death row, being completely without excuse.  They know judgment is certain.  They badly need the Savior!  Then, we may move to Romans chapters 3-12, or other Bible passages, with the Gospel, the "good news," and with all of the wonderful details.

Romans chapter 10:1-13 is often used for specifics to help a person see what they must do to become a Christian: 

1 Brethren, my heart's desire and prayer to God for Israel is, that they might be saved. 2 For I bear them record that they have a zeal of God, but not according to knowledge.

3 For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God. 4 For Christ is the end of the law for righteousness to every one that believeth.

5 For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them. 6 But the righteousness which is of faith speaketh on this wise, Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ down from above:) 7 Or, Who shall descend into the deep? (that is, to bring up Christ again from the dead.)

8 But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is, the word of faith, which we preach; 9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.

10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. 11 For the scripture saith, Whosoever believeth on him shall not be ashamed.

12 For there is no difference between the Jew and the Greek: for the same Lord over all is rich unto all that call upon him. 13For whosoever shall call upon the name of the Lord shall be saved.

See my page They Came to Jesus! for a handy way to help a person come to Jesus Christ by viewing three men in the New Testament who do just that, right before our eyes.