Was Jesus born only to die?

Yes, Jesus was born to die. John Piper wrote an excellent book covering this topic entitled, 50 Reasons Jesus came to Die. However, while we are all born to die (Heb. 9:27), there is much more to speak about than just death. Now 'for the rest of the story' (well, at least some of it):

While we should emphasize Christ's death, Scripture teaches us that Christ did more than just die! While Jesus' death is of course of all consuming importance, so was his whole life (John 21:25), his resurrection (1 Cor. 15:1-4, 19-20), and the fact that he ascended (Acts 2:32-35; Eph. 1:20; Heb. 10:12; 1 Pet. 3:22). In 1 Corinthians 2:2, which you pointed to as the 'complete Gospel,' Paul also added, 1 Corinthians 15:1-8, which included Christ's death, burial, resurrection and I Corinthians 15:25, which includes his present reign in heaven (2 Cor. 5:16; Eph. 1:20-23; Col. 3:1; cf. 1 Pet. 3:22, et. al.).

As Paul wrote to the Church at Rome, "Who is he that condemns? Christ Jesus, who died - more than that, who was raised to life - is at the right hand of God and is also interceding for us" (Rom. 8:34; cf. Rom. 6:8-10; 1 Cor. 15:14-22). Note, that Paul brings out the point that yes indeed Jesus died, but he adds "more than that" and speaks of Jesus' rising from the dead, being seated with God, and praying for his people. So, when we speak of the importance of the sacrifice of our Lord, when we talk of his death, when we mention his grave, we should also understand that without his incarnation and life he would/could not have died, and without his death he would not have required being raised, and he would not be at the right hand of God, praying for his church, etc. Jesus' death thus speaks of his entire life - even going back into all eternity (2 Tim. 1:9; cf. Rom. 8:29-30; Eph. 1:4-5, 11) - as God of very God became incarnate (John 1:14; Rom. 8:3; Gal. 4:4-5; Phil. 2:5-11; Heb. 2:14). 'Unto us a child was born, unto us a Son was given' (Isa. 9:6). So, when we speak of Christ's death, the whole spectrum of his existence should come to mind, he is eternal, he lived, he died, he lives, he lives forevermore (Rev. 1:17-18).

While Jesus came to die, he came to do so 'much more' (Rom. 8:34; cf. John 21:25). He is God in the flesh (John 1:14). He lived a perfect sinless life (Heb. 4:15). He is the greatest teacher (Matt. 7:29; John 3:2). He set a perfect example (Eph. 5:1). He performed miracles (Matt. 8:16-17; Mark 1:40-45; Luke 8:40-42, 49-56; John 4:43-54, etc.). But, he also fulfilled all righteousness (Matt. 3:13-15). While he died for many reasons, one is saved not only by his death, but his life as well (Rom. 5:10). C. S. Lewis said it well: "The Son of God became a man that men might become sons of God." His life is imputed to us that we may live (cf. Rom. 4:3, 5; 2 Cor. 5:21; Jam. 2:23, etc.). He died that his elect may live. What a great salvation (Heb. 2:3).

So, while your crucifix "reminds" (not "tells;" Scripture tells us the truth - Psa. 86:11; 119:160; Dan. 10:21; John 1:14; 8:31-32; 17:17; Jam. 1:18) you of "a" truth; it is not the "whole" truth and nothing but the truth. The whole truth is found in the whole counsel of God (Acts 20:27; cf. Psa. 40:10; Jer. 26:2; Ezek. 40:4; Acts 20:20). Here, from beginning (Gen. 1:1) to end (Rev. 22:21), from Genesis (Gen. 3:15) to Revelation (Rev. 12), we see God's redemptive story. We can see types of Jesus in the lives of Adam, Abel, Noah, Abraham, Moses, David, etc. We see God's plan, Person, and purpose. While there is much that could be written here, part of God's plan was to save his people from their sins (Matt. 1:21) through his Son (John 1:29), to accomplish his purpose of bringing glory to himself (Eph. 3:21; Phil. 1:11), according to the good pleasure of his will (Eph. 1:4-5, 11; 2 Tim. 1:9). Therefore, the death of Christ should remind us of the whole story from beginning to end.

So, only when we preach "the whole counsel of God" (Acts 20:27), do we fully preach "Christ and him crucified" (1 Cor. 2:2).

As Paul wrote, "Beyond all question, the mystery of godliness is great: He appeared in a body,
 was vindicated by the Spirit, 
was seen by angels,
 was preached among the nations,
 was believed on in the world,
 was taken up in glory" (1 Tim. 3:16).

While Jesus was born to die, he was not born "only" to die!

As to the crucifix that some wear (of which you did not inquire), I would consider the Confessions, with their Scriptural proofs, a good place to begin:

The Westminster Larger Catechism:

Question 103: Which is the first commandment?

Answer: The first commandment is, Thou shall have no other gods before me.

Question 104: What are the duties required in the first commandment?

Answer: The duties required in the first commandment are, the knowing and acknowledging of God to be the only true God, and our God; and to worship and glorify him accordingly, by thinking, meditating, remembering, highly esteeming, honoring, adoring, choosing, loving, desiring, fearing of him; believing him; trusting, hoping, delighting, rejoicing in him; being zealous for him; calling upon him, giving all praise and thanks, and yielding all obedience and submission to him with the whole man; being careful in all things to please him, and sorrowful when in anything he is offended; and walking humbly with him.

Question 105: What are the sins forbidden in the first commandment?

Answer: The sins forbidden in the first commandment are, atheism, in denying or not having a God; idolatry, in having or worshiping more gods than one, or any with or instead of the true God; the not having and avouching him for God, and our God; the omission or neglect of anything due to him, required in this commandment; ignorance, forgetfulness, misapprehensions, false opinions, unworthy and wicked thoughts of him; bold and curious searching into his secrets; all profaneness, hatred of God; self-love, self-seeking, and all other inordinate and immoderate setting of our mind, will, or affections upon other things, and taking them off from him in whole or in part; vain credulity, unbelief, heresy, misbelief, distrust, despair, incorrigibleness, and insensibleness under judgments, hardness of heart, pride, presumption, carnal security, tempting of God; using unlawful means, and trusting in lawful means; carnal delights and joys; corrupt, blind, and indiscreet zeal; lukewarmness, and deadness in the things of God; estranging ourselves, and apostatizing from God; praying, or giving any religious worship, to saints, angels, or any other creatures; all compacts and consulting with the devil, and hearkening to his suggestions; making men the lords of our faith and conscience; slighting and despising God and his commands; resisting and grieving of his Spirit, discontent and impatience at his dispensations, charging him foolishly for the evils he inflicts on us; and ascribing the praise of any good we either are, have, or can do, to fortune, idols, ourselves, or any other creature.

Question 106: What are we specially taught by these words before me in the first commandment?

Answer: These words before me, or before my face, in the first commandment, teach us, that God, who sees all things, takes special notice of, and is much displeased with, the sin of having any other God: that so it may be an argument to dissuade from it, and to aggravate it as a most impudent provocation: as also to persuade us to do as in his sight,: Whatever we do in his service.

Question 107: Which is the second commandment?

Answer: The second commandment is, Thou shalt not make unto thee any graven image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth: Thou shalt not bow down thyself to them, nor serve them: for I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me; and showing mercy unto thousands of them that love me, and keep my commandments.

Question 108: What are the duties required in the second commandment?

Answer: The duties required in the second commandment are, the receiving, observing, and keeping pure and entire, all such religious worship and ordinances as God has instituted in his Word; particularly prayer and thanksgiving in the name of Christ; the reading, preaching, and hearing of the Word; the administration and receiving of the sacraments; church government and discipline; the ministry and maintenance thereof; religious fasting; swearing by the name of God, and vowing unto him: as also the disapproving, detesting, opposing, all false worship; and, according to each one's place and calling, removing it, and all monuments of idolatry.

Question 109: What are the sins forbidden in the second commandment?

Answer: The sins forbidden in the second commandment are, all devising, counseling, commanding, using, and anywise approving, any religious worship not instituted by God himself; tolerating a false religion; the making any representation of God, of all or of any of the three persons, either inwardly in our mind, or outwardly in any kind of image or likeness of any creature: Whatsoever; all worshiping of it, or God in it or by it; the making of any representation of feigned deities, and all worship of them, or service belonging to them; all superstitious devices, corrupting the worship of God, adding to it, or taking from it, whether invented and taken up of ourselves, or received by tradition from others, though under the title of antiquity, custom, devotion, good intent, or any other pretense: Whatsoever; simony; sacrilege; all neglect, contempt, hindering, and opposing the worship and ordinances which God has appointed.

Question 110: What are the reasons annexed to the second commandment, the more to enforce it?

Answer: The reasons annexed to the second commandment, the more to enforce it, contained in these words, For I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me; and showing mercy unto thousands of them that love me, and keep my commandments; are, besides God's sovereignty over us, and propriety in us, his fervent zeal for his own worship, and his revengeful indignation against all false worship, as being a spiritual whoredom; accounting the breakers of this commandment such as hate him, and threatening to punish them unto divers generations; and esteeming the observers of it such as love him and keep his commandments, and promising mercy to them unto many generations.

The Heidelberg Catechism:

Q&A 94

Q. What does the Lord require in the first commandment?

A. That I, not wanting to endanger my own salvation, avoid and shun all idolatry,1 sorcery, superstitious rites,2 and prayer to saints or to other creatures.3

That I rightly know the only true God,4 trust him alone,5 and look to God for every good thing6 humbly7 and patiently,8 and love,9 fear,10 and honor11 God with all my heart.

In short, that I give up anything rather than go against God's will in any way.12

1 1 Cor. 6:9-10; 10:5-14; 1 John 5:21
2 Lev. 19:31; Deut. 18:9-12
3 Matt. 4:10; Rev. 19:10; 22:8-9
4 John 17:3
5 Jer. 17:5, 7
6 Ps. 104:27-28; James 1:17
7 1 Pet. 5:5-6
8 Col. 1:11; Heb. 10:36
9 Matt. 22:37 (Deut. 6:5)
10 Prov. 9:10; 1 Pet. 1:17
11 Matt. 4:10 (Deut. 6:13)
12 Matt. 5:29-30; 10:37-39

Q&A 95

Q. What is idolatry?

A. Idolatry is having or inventing something in which one trusts in place of or alongside of the only true God, who has revealed himself in the Word.1

1 1 Chron. 16:26; Gal. 4:8-9; Eph. 5:5; Phil. 3:19

Lord's Day 35

Q&A 96

Q. What is God's will for us in the second commandment?

A. That we in no way make any image of God1 nor worship him in any other way than has been commanded in God's Word.2

1 Deut. 4:15-19; Isa. 40:18-25; Acts 17:29; Rom. 1:22-23
2 Lev. 10:1-7; 1 Sam. 15:22-23; John 4:23-24

Q&A 97

Q. May we then not make any image at all?

A. God can not and may not be visibly portrayed in any way.

Although creatures may be portrayed, yet God forbids making or having such images if one's intention is to worship them or to serve God through them.1

1 Ex. 34:13-14, 17; 2 Kings 18:4-5

Q&A 98

Q. But may not images be permitted in churches in place of books for the unlearned?

A. No, we should not try to be wiser than God. God wants the Christian community instructed by the living preaching of his Word 1 - not by idols that cannot even talk.2

1 Rom. 10:14-15, 17; 2 Tim. 3:16-17; 2 Pet. 1:19
2 Jer. 10:8; Hab. 2:18-20

After, a study of the biblical data above, then consider reading "Images of Christ."