My prayers include regular and spontaneous. If someone comes to my mind, I pray for that person right away. If I drive on high way and see some accident, I pray for whoever is involved right away. If I heard some tragedy in news, I pray for it right away. That is my spontaneous prayer.
I also have my regular prayers. I pray for my family, my priests, some friends and relatives daily. I pray for Pope, our Church, our country often, not every single day but should be. I pray for my church friends, my parish, my CCD students, and CAF prayer requests whenever I think about it. If someone asks for my prayer, I usually pray for the person right away and whenever I remember afterwards unless I made a commitment to pray everyday.
To pray for everyone in the world or every intention in the box is very general. God likes us to pray specifically. And I believe to be specific is more effective.
If I were committed to a long prayer list, I probably will categorize it, for example, put all health related in one group, finance related in another and say my rosary for each category. I will tell the Lord in the beginning that this Rosary is for so and so and so to receive healing, or this Rosary is for so and so and so to find employment or solve financial problem, etc…
That is just my preference.
But on the top of petition and intercession prayer, keep in mind the prayer of thanksgiving and praises, the prayer of repentance and act of contrition. I am trying my best not to approach the throne of Divine Mercy only asking for favor either for self or for others. Keep in mind our Lord wants the most is our love. So, no matter how long the prayer list is, love Him first, spend some quiet time with Him, adore Him, thank Him, praise Him, glorify Him, bless Him. Tell Him you love Him.