Three times in I Timothy 6 Paul uses the term "godliness."
First, Paul criticizes those who consider "godliness is a means to financial gain" (vs. 5).
Perhaps you have seen this approach employed by some (often television) preachers. They hold out the lure of financial prosperity as an inducement to follow the gospel. "Want a new car? A new home? A diamond bracelet? Name it and claim it in faith. God wants you to be wealthy!" While this teaching is seductive and contains a kernel of truth (God does want us to be blessed), the mistake is made that godliness is the path to financial gain. Christians seek after godliness (becoming righteous like God, or Christlike) not because of how we can profit from it, but because it is right and true and good. God wills it, not for our financial wealth but for our spiritual health.
But, Paul points out, "Godliness with contentment is great gain" (vs. 6).
Gain is not evil - it's just the emptiness of worldly wealth as a chief end that is wrong. Instead of financial gain, we should be focused on contentment and holiness. This section of I Timothy leads into the famous (and often misquoted verse), "For the love of money is a root of all kinds of evil" (vs. 10). Loving money and chasing after it doesn't lead to life and happiness, but to being pierced with many griefs (vs. 10).
Finally, Paul tells Timothy, "Flee from all this, and pursue righteousness, godliness..." (vs. 11)
So if we should not set our sights on money, what then? Our pursuit should be goodness, righteousness, godliness. It may sound trite, but being good for goodness' sake ought to be enough. If we are only good for rewards we hope to get or punishments we hope to avoid, what does that say about us? And what happens if, in heaven, those rewards and punishments cease to be a factor? I often think that what God desires of us is to become truly Christlike in our character so that, if all the restraints and inducements were to be removed, we would still be the same kind of good person that we are striving to be with those things.
Brothers and sisters, let us pursue righteousness, godliness, faith, love, endurance and gentleness!