"that I may be His own and live under Him in His kingdom"

This part of the meaning usually gets too little air time, but this part is where the rubber really meets the road as far as your day-to-day life is concerned. "that I may be His own and live under Him in His kingdom" is a brief description of what your new life in Christ looks like.

Notice I said LOOKS like; not WILL look like.

Even though you are still living in the same body you were born into and even though you still struggle with sin, your new, eternal life has already begun. It begins the hour you first believe what God has done for us and our salvation in Jesus Christ.

So you are "His own" RIGHT NOW, and you "live under Him in His kingdom" RIGHT NOW. And living in His kingdom means serving Him "in everlasting righteousness, innocence, and blessedness."

This is the life that Jesus saved you for. It has already begun and it will continue forever.

Even so, some might be tempted to say, "Wait! Even though I still suffer the effects of sin in this life and my body dies like it would have anyway, I'm expected to live 'in everlasting righteousness, innocence, and blessedness.'?  What's He done for me lately?"

Now trading off "what I've got to do" in exchange for "what I get for it" like that is the world's way of thinking.  But if we need to discuss it under those terms, let's do it. Before you were called into Christ, you were dying and suffering along the way and it would all end in eternal torment. Now (in Christ) you have eternal life and freedom from all pain and suffering in the end. So even though you don't see the full benefit of your calling until the Last Day, you DO gain something from following Christ! And it's not just a little something... it's something that lasts forever!

When Paul was exhorting the Romans to avoid sexual immorality, he wrote: "Do you not know that your body is a temple of the Holy Spirit within you, whom you have [now] from God? You are not your own, for you were bought with a price. So glorify God in your body." (1 Corinthians 6:19-20)

In other words, God has bought your 'everlasting righteousness, innocence and blessedness' with the blood of Christ. He gives it to you, and He deserves it from you. Both are true!