Your prayer has been received with thankfulness, and your desire to pray as the Lord taught His disciples is itself a work of grace. To seek first the Father, His name, His kingdom and His will, and then to ask for our daily needs, forgiveness and deliverance, is the right order. It keeps the heart fixed on God before it turns to itself.
You are right to see this prayer not as words to be repeated without thought, but as a pattern to shape the heart. When you say Our Father, remember what has been given to you. You were once far off, in darkness and under judgment, yet through Christ you have received forgiveness, adoption as a son or daughter, the gift of the Holy Spirit and the inheritance of the kingdom. To call God Father, even Abba, is a privilege bought by the blood of Christ, His burial and resurrection, and His ascension to pour out the Spirit. Pray it with reverence and confidence, knowing you are heard as a child.
To pray Hallowed be Your name is to ask that His name, which is gracious and compassionate, may be honored in your thoughts, words and actions, and that your life would not cause it to be dishonored before others. To pray Your kingdom come and Your will be done is to ask for His righteousness, peace and joy to reign in you through the fruit of the Spirit, love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self control, and for strength to walk humbly, to do what is just and to love mercy. It is also to ask for power to live a holy life, to bear fruit, to make disciples, and to look with hope for the day when Christ returns and His kingdom is fully revealed.
When you ask for daily bread, ask for what you need for health and for service, not for excess. We are taught to make provision for the flesh for health, not to fulfill its lusts. God knows your spiritual, physical and material needs and has promised to supply them so that you may love Him with all your heart and love your neighbor as yourself.
When you pray forgive us as we forgive others, come honestly, naming your sins before God and trusting His mercy, and at the same time release those who have sinned against you, praying for them and entrusting judgment to God who alone saves and judges. Blessed are those whose sins are forgiven and covered, and that blessedness brings not only pardon but glory.
When you pray lead us not into temptation but deliver us from evil, remember that no temptation has overtaken you except what is common to humanity, and God is faithful. He will not let you be tempted beyond what you can bear, but will provide a way of escape so that you can endure it. He often allows a trial to remain for a time not because He withholds good, but so that you will persevere and keep fleeing to Him, as a loving father allows a fear to draw his child closer to his arms. He gives patience and He brings release in due time. Ask also for protection from deception, from evil people and from the evil one, and trust His power to keep you.
Continue in this pattern with understanding, with earnest expectation and with perseverance. If you do not receive at once, keep praying. If you do receive, keep praying still with thanksgiving. For His is the kingdom and the power and the glory forever, and all His promises are yes and amen in Christ. May He deepen your knowledge of His names, establish His kingdom in your life and home, and keep you walking in His will until the day He comes.