You are right when you say Christians don't believe in reincarnation–but I hope you'll understand why we don't, because a very important truth is behind our conviction.
Christians reject reincarnation for two main reasons. The first is because the Bible does not teach it, and in fact makes it clear that when we die we don't return to earth again but enter eternity–either with God in heaven or apart from God forever. The Bible says, "Man is destined to die once, and after that to face judgment" (Hebrews 9:27).
The second reason Christians reject reincarnation is because Christ has paid the full penalty for our sins–totally and completely. He did this by His death on the cross for us. You say you hope to become perfect some day in another life–but Jesus has already made us perfect in God's eyes, by taking away all our sins! The Bible says, "But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ" (1 Corinthians 6:11).
Think of it: Every sin you have ever committed can be completely cleansed, if you will turn to Christ in repentance and faith! Don't be deceived by a false hope, but put your faith and hope in Christ today.