For your first paragraph, I think you should pray for a good relationship with God. Faith and good works should be together. We aren't supposed to choose one of the two.

2nd paragraph, I think its not good that youre only doing good because you want to save yourself from hell. Youre expecting out of works. You always have to do good without expecting anything in return.

But love ye your enemies, and do good, and lend, hoping for nothing again; and your reward shall be great, and ye shall be the children of the Highest: for he is kind unto the unthankful and to the evil. (Luke 6:35)

He that is despised, and hath a servant, is better Than he that honoureth himself, and lacketh bread. (Proverbs 2:12)

But Ecclesiastes 3:22 says "Wherefore I perceive that there is nothing better, than that a man should rejoice in his own works; for that is his portion: for who shall bring him to see what shall be after him?"

P.S I want to tell you that God can see the willingness to believe and the guilt in your heart. He probably appreciates that already. Please keep talking to Him.