Todd, Thanks for starting this topic. First of all, I must mention that Matthew 6:33 changed my life 50 years ago. I have been fascinated with the topic ever since. Just to learn that the Kingdom of God was more than a future 1,000 year reign of Christ started me on a life-long journey that continues to this day. I don't claim to fully understand it all but having a focus on the kingdom of God as a priority has enriched me greatly.
The Young's Literal Translation encouraged me as well. John 3:3 is very interesting:

Jesus answered and said to him, 'Verily, verily, I say to thee, If any one may not be born from above, he is not able to see the reign of God;' 

Back then, when I fully and more completely surrendered my life to Jesus, it was as if my eyes were opened, and I could see God's work in my life and in the world more clearly. I still believe in a future demonstration of the reign of God on earth, but now I know that it began over 2,000 years ago exactly as Jesus said it would.

While Jesus did not exactly give a dictionary definition of the kingdom of God, He taught in word and deed many things to help us understand it. Even as a young man, I understood enough about it to turn my life around and to experience His righteousness, peace and joy in the Holy Spirit!