Answer: The kind of sacrifice which pleases God is a living sacrifice--a holy sacrifice, a pleasing sacrifice, (verse 1).
MORE INFORMATION AND/OR OTHER SCRIPTURE REFERENCES:
The Christian as a living sacrifice to God could be a contrast to the dead animal sacrifices offered to Him in Old Testament worship, or it could be "living" as in the sense of having a new life in Christ after having been buried with Him through baptism into death and being raised to walk a new life (Romans 6:4).
Romans 6:13: "Do not offer the parts of your body to sin, as instruments of wickedness, but rather offer yourselves to God, as those who have been brought from death to life; and offer the parts of your body to Him as instruments of righteousness."
Romans 6:16: "Don't you know that when you offer yourselves to someone to obey him as slaves, you are slaves to the one whom you obey--whether you are slaves to sin, which leads to death, or to obedience, which leads to righteousness?"
Romans 6:19: "I put this in human terms because you are weak in your natural selves. Just as you used to offer the parts of your body in slavery to impurity and to ever-increasing wickedness, so now offer them in slavery to righteousness leading to holiness."
1 Corinthians 6:20: "you were bought at a price. Therefore honor God with your body."
1 Peter 2:5: "you also, like living stones, are being built into a spiritual house to be a holy priesthood, offering spiritual sacrifices acceptable to God through Jesus Christ."