Romans 6:12-14 meaning

The word Therefore always indicates that the statements following it are fundamentally tied to the evidence that preceded it. Before the Therefore, Paul has laboriously explained how Christians can live a resurrection life now that they are dead to sin (through faith in Jesus's death and resurrection). In doing so Paul is both instructing the Roman believers (whose faith is spoken of throughout the entire world, Romans 1:8) as well as refuting the slanderous charges against his teaching.

After the Therefore, Paul warns the Roman Christians against returning to their old sinful ways. The statement do not let sin reign in your mortal body so that you obey its lusts (v 12) implies that it is still possible for a Christian to live sinfully and obediently toward their selfish desires. This is why Paul continuously reminds the Roman believers that they have a new life in Christ, that they are freed from their old ways. Additionally, Paul is dealing with slanderous claims from competing Jewish "authorities" who are in Rome and are mispresenting his teaching to say that sinning is good because God will be glorified in forgiving it. Paul corrects this false notion throughout his letter to the Romans. This letter to the Roman believers will also help Paul's ministry partners Aquila and Priscilla, who host a church in their house in Rome, to counter the arguments of the competing Jewish "authorities" (Romans 16:3; Acts 18:2, 18, 26).

Yes, God will always forgive our sins, but that does not mean we should sin even more. We should no longer go on presenting the members of our body to sin as instruments of unrighteousness (v 13) when we can enjoy living the new life we've been given.

Be careful, Paul is saying, not to live as if you were still dead, but present yourselves to God as those alive from the dead (v 13). Having been spiritually given a resurrected life in Christ, Christians are called to live as living people, rather than living the life of death sin brings. Paul presents two distinct choices: live as a dead person whose body is a slave to its own lusts and ruled by sin, or present yourself to God as a living person, and your members [body] as instruments of righteousness to God (v 13).

This looks like us living in harmony with the way God made us, and other people, and the world. To live justly we walk in faith by the power of the Spirit. Paul discusses walking in the Spirit at length in Chapter 8.

In verse 14, Paul brings his argument back to the distinction that Christians are not under the law. We are justified by grace, not the law. We received this grace by our faith in Jesus's death and resurrection (Ephesians 2:8). Sin is still in the world and in us. Christians have been empowered to choose which master to serve: sin or God. Paul is not talking about being justified before God as a legal status; Christians are already justified in the eyes of God because of Christ's sacrifice on our behalf. We put our faith in Christ's death and resurrection and have been saved from Hell and death. But now, as believers, we still have to choose constantly whether to live justly in our daily lives: For sin shall not be master over you, for you are not under law but under grace (v 14). 

The choice is whether we want to live a life which brings harmonious living or live in death which brings unrighteousness. That's the choice. That's the consequence.