The following is how I see true worship. Worshipping God in Spirit and in Truth:-
First of all true worship would be an understanding and obedience to the two commandments Jesus gave us in Mark 12:30/31:
"And thou shalt love the Lord thy God with all thy heart, and with all thy soul and with all thy mind, and with all thy strength: this is the first commandment.
And the second is like, namely this, Thou shalt love thy neighbour as thyself. There is none other commandment greater than these."
And your question...
Also do we worship God because of who he is?
or because of what he can do in our lives?...
Until by the Grace of God, the cross has had its effect in our lives, in that we give up all for Christ, and continue to do so, only then are we delivered from self deception and false worship. For if there is something in our life which comes before Christ, we become easily self-deceived into believing we are serving and worshipping God, but in fact, we are worshipping that which we are holding onto, and/or our self desires.
Our safeguard is that we see the value of the Cross (understanding the Wisdom of God), by watching ourselves that we remain humble before Him, and open to conviction by the Holy Spirit, that nothing is taking our love away from Him (the first commandment to love God with ALL our heart etc.).
Then we worship Him because we love the truth (which sets us free)therefore we love Him....and worship Him in Spirit and in truth.