In a nutshell, I think that if you are filled by the Holy Spirit, and you have a new heart with new desires and affections (this idea is right he way through the bible regarding salvation), then you will naturally not want to abuse grace...
I believe that salvation comes about the same way as it did in Act 2: Indwelling and empowering of the Holy Spirit (v4) --> Public bible preaching (or investigation of the bible if its personal) (v19-21) --> Preaching/reading of Christ crucified (v22-36) --> response of true Repentance. I always point this out when I am teaching this, that not once did Peter ever mention repentance until the people's hearts were ready... the people were the ones that came to him once he was done, having been cut to the heart, and ask what they were to do about their predicament of offending a Holy God...Peter only then replies that they need to “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.” (Acts 2:38-39) Forgiveness of sins means that you need faith in the Forgiver. The rest of Acts 2 shows the results.
But in a wider understanding of what that term means, I will come clean and say that I believe that those who are saved are actually chosen before the creation of the world (Ephesians 1:3-4) (as well as those not destined for that)....of course doesn't mean we shouldn't spread the good news...we have no idea who those people are (1 Corinthians 1:23-24). In that sense, I believe in the idea of irresistible grace, that is, that once you know God you don't want anything else; which taken to the nth degree means that you can't lose your salvation. At the same time I believe that it is still each persons choice to follow or not, and both of those ideas are in the bible. However, the idea that we have to work at all by ourselves for salvation is not in the bible as you already know.
That was an ancient heresy called pelagianism which is the belief that man is still able to and must cooperate with God to accomplish his salvation. Pelagianism does not believe in total depravity or the need for grace to restore us from that state. The bible always talks of total depravity and the need for grace to initiate our restoration from it.