When you begin your prayer time, pray around the passage you have just read. Prayer should always be prepared and inspired by the Word. Then after you have finished praying around the scriptures, you can start making a list of requests others have given you and also of your own needs.
If you are really struggling, you will tend to be more sympathetic toward yourself and want to list more items for yourself. But don’t do that. Do the opposite. Pray more for others. Paul tells us that we are to esteem others better than ourselves; to regard their interest’s more than our own (Phil 2:3-4). And if you do this, especially if you are feeling down, God will bless you and lift you up. That has been my experience. When I have felt down, after I have prayed for others for a while, God has lifted me up.
When you list the requests of others, be careful not to read into them or analyze them. It should be your intent to pray for them exactly as they have made their request. Then, as you begin praying for them, the Holy Spirit may move you to pray for other things, deeper things. He will show you exactly what they need and how to pray for them (Rom. 8:26).
As for your own requests, I think the most important things to pray about is over what God has just spoken to you about in His Word. Pray over that first. Then list and pray over any other concerns you have. Pray over everything you may be anxious about (Phil. 4:6). Pray for anything you think you need or that you desire. You can feel free to pray about anything. Nothing is off limits.
As you are praying, however, God will show you what things you really need and what things would actually not be beneficial for you to have (1 Cor. 6:12). I have experienced that the more I meditate on God’s Word, and the more I pray, the more He will reveal to me those things He wants me to have and pray about. Here then is a good principle of prayer: the more we pray the more we will know how to pray.