A Heart Sacrifice
You do not delight in sacrifice, or I would bring it; you do not take pleasure in burnt offerings. My sacrifice, O God, is a broken spirit; a broken and contrite heart you, God, will not despise. Psalm 51:16-17 (New International Version, NIV)
This tells us what God does and does not want. Offerings are called sacrifices; a sacrifice is what you offer to God. A true sacrifice is to give Him your heart. Offer your heart to God, broken and repentant for sin. As a sacrifice to God, give yourself to Him wholly and completely. A repentant, contrite heart will never be rejected by God.
God sees when we mean business with Him. He knows when being right with Him is what matters most to us. Then our heart is cleansed and made right. Then we can offer ourselves fully in worship and service to Him. First, we let God minister to us, cleaning up and repairing our hearts. Then we can minister to Him out of a pure heart. Then, we can go and minister to others. This is how we become living sacrifices, holy and acceptable to Him- which is our reasonable service, worship, and offering. This is pleasing to God.
I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. Romans 12:1 (KJV)