There is a due order in these things. The text you bring from Romans settles the matter well, for it places heart-belief first and mouth-confession following. Yet observe how the one living root sends up two green shoots, for faith and repentance spring up together in the soul that is born from above. You cannot have the faith which saves without the repentance which renounces sin, nor the repentance which is genuine without the faith which lays hold on Christ. They are, towards one another, like the Siamese twins, bound together by a living cord which no man may cut asunder.
But consider well what manner of repentance this is that accompanies salvation. There is a repentance of the flesh worked by fear of judgment, yet it leaves the heart unchanged and never gives God glory. True repentance, the gift of His grace, makes the sinner look upon the Christ he has pierced and mourn for him with a sorrow that needs not to be repented of. It casts down every idol and enthrones Jesus as sole Master of the heart. This repentance is not a condition you perform to win mercy; it is itself a covenant blessing, one of the free gifts of His grace, and whoever has it may rest assured that the work of salvation has been already begun in his soul.
Do not look within to measure whether your repentance be deep enough or your faith strong enough. The least faith saves if it be true faith, faith which begins and ends with Jesus. It is not upon our faith, our repentance, our prayers, or our conquests of sin that we rest; right away from anything that comes from us or to us we look to Jesus, who is all our salvation, the Alpha and Omega. That faith which believes in the probable is anybody's faith; publicans and sinners can so believe. But to trust Christ alone for everything, to treat all God's Word alike as sure, to roll your burden upon the Lord in the common matters of daily bread and household cares, this is the faith of God's elect.
Then let confession follow as the fruit upon the branch. With the heart man believes unto righteousness, and with the mouth confession is made unto salvation. The same things which are the basis of our salvation become the subject of our confession before men. Do not dissociate the word of confession from the action, but say it unmistakably, "I am the Lord's." If you are timid and slow of speech, condemn not yourself; some who cannot speak their confession may joyfully write it. The essential matter is that your faith be your own, your repentance your own, your coming to Christ your own. No man can perform your religion for you.
Read the Scriptures with earnest desire, beginning where you have been directed. Yet remember that no diligence in reading, no amount of study, can take the place of that simple looking unto Jesus which is the work of the Spirit. We through the Spirit wait for the hope of righteousness by faith. The Holy Spirit's office is to glorify Christ, and He could not do this if salvation by faith were an imperfect matter. Rest certain that faith in Jesus Christ as the ground of salvation cannot be opposed to the Spirit's work, because that faith is based upon the Spirit's own testimony concerning Christ. May He lead you into the full assurance of understanding, and may sweet Sister Repentance become to you such charming company that you will rejoice to walk with her even unto the gates of pearl.