Christ said that what he came to tell us, what the gospel is, is "repent, for the kingdom of heaven is at hand" (Matt 3:2 and 4:17). When we repent of sin Christ will forgive our sin and we can then live with God forever.
Sorry but I just need some more clarification on your quote above.
You quote 2 Bible verses then follow that with when we repent of sin.
Neither of these verses mention to repent of sin.
Matthew 3:2
2 and saying, “Repent, for the kingdom of heaven is at hand!”
Matthew 4:17
17 From that time Jesus began to preach and to say, “Repent, for the kingdom of heaven is at hand.”
Let's look at the verse where Jesus said what sin we should repent off.
John 16:5-9
The Work of the Holy Spirit
5 “But now I go away to Him who sent Me, and none of you asks Me, ‘Where are You going?’
6 But because I have said these things to you, sorrow has filled your heart.
7 Nevertheless I tell you the truth. It is to your advantage that I go away; for if I do not go away, the Helper will not come to you; but if I depart, I will send Him to you.
8 And when He has come, He will convict the world of sin, and of righteousness, and of judgment:
9 of sin, because they do not believe in Me;
Look at verse 9 what is the sin to repent off?
Unbelief in him.
Now when we do that as Paul says
Romans 10:8-13
8 But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): 9 that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. 10 For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. 11 For the Scripture says, “Whoever believes on Him will not be put to shame.” 12 For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him. 13 For “whoever calls on the name of the Lord shall be saved.”
Then we have the definition of faith that saves.
Nothing more or nothing less.
Jesus said that.
Now that does not mean that actions after such confession will not follow.
Once a genuine confession has been made then one will want to be like Jesus.
It is the outworking of biblical faith.