What is easiest for me, since I have been praying the LOTH for awhile now is begin my day with the LOTH,
The LOTH allows the Office of Reading and Morning Office to be combined. I have been on retreats where the congregation goes immediately from Morning Office straight into the Mass. The closing prayer for the Morning Office is often the same as the opening prayer for the Mass.
A spiritual director of mine pointed out the problem with that approach. The LOTH honors the hours of the day while the Mass is outside of time.
When I was in 1st grade, long before I knew anything about the LOTH, my first grade nun said a good time to pray the Morning Offering was when I was kneeling on the floor to get my shoes out from under my bed. I can’t keep my shoes under my current bed.
I pray the LOTH followed by Morning Prayer, Abandonment to God’s Providence, and Prayer to my Guardian Angel. If I remember, I will have prayed the Angelus before LOTH. Afterwards, I pray the Little Crown of the Blessed Virgin Mary.
Depending on my schedule, I will read the daily Mass reading plus scriptural readings either now, or later if I have an early morning appointment.
This morning routine, with scripture readings takes about an hour.
When working, the scripture readings were after work. I prayed the Guardian Angel prayer with my grandson while he waited for the school bus in the morning.
It doesn’t matter whether you pray the morning offering first, or the LOTH first.
The morning offering simply works better for me after the LOTH and before the Little Crown of the Blessed Virgin Mary. I end with the prayer of Unity for Christians and Radiating Christ before reading Scripture.