Giving our life to Christ?

It's commonly suggested that when we become a christian we are 'giving our lives to Christ' but i would say that we are actually receiving his life as he enters us and empowers us with his 'zoe' life. God is propositioning us with his gospel message to come to him and receive his life free of charge and our response is either yes or no. It's really not about what we give up for him but simply receiving his offer of righteousness and the indwelling of his spirit. The gospel contains no conditions other than to believe however we do see that within the book of acts people were instructed to repent and believe but repent means simply to change your mind 'metanoia' change what you have previously thought was the way to God through good works and believe the gospel message of his righteousness becomes mine when I believe!