My best advice for new teachers is to memorise the sun salutation. Start with the hatha version because this is the easiest on the beginner student’s body.
I often get complaints and grimaces from my trainees because they don’t want to memorise the classical sun salutation. They claim they get confused with right and left etc.
It is true that the ashtanga vinyasa sun salutation is easier to memorise for the teacher. There is no right or left side to think of. However, it is harder to perform correctly. Chaturanga Dandasana is not a beginner pose and done incorrectly can cause rotator cuff injury. The ashtanga sun salutation is a strength builder.
The hatha sun salutation allows the practitioner to move and warm up all the joints of the body from ankle to neck. There is not a great deal of flexibility or strength needed for the hatha sun salutation. Everyone can do it. There is very little need to modify it.
Did you know the sun salutation also comes with mantras?