Is there such a prayer that could be a common Christian prayer and a model for all prayers?
This is the Lord's prayer.
What is the Lord's Prayer?
The prayer that our Lord Jesus Christ taught to the apostles and which they passed on to all believers.
How is it read?
Our Father, Who art in Heaven,
Hallowed be thy name,
Thy kingdom come;
Thy will be done as it is in heaven and on earth.
Give us this day our daily bread;
and forgive us our debts, just as we forgive our debtors;
and do not lead us into temptation,
but deliver us from evil.
For Yours is the kingdom, and the power, and the glory forever. Amen (Matt. 6:9-13).
To more conveniently consider the Lord's Prayer, how can you divide it?
For invocation, seven petitions and doxology.