To do it right: Sonotube to below frost line, with the post starting ON TOP of the concrete (not in it).
I do this for any addition, attached deck, etc. where I want it to pass an inspection.
For a simple unattached shed and to keep it cheap and simple? Concrete piers on top of a few inches of gravel that is below the soil level, like these:
https://www.homedepot.com/p/7-3-4-i...REC-_-pipsem-_-100321948-_-204827028-_-NI have built 2 sheds in the frost-heave of Colorado, both over 20 years old, both sitting square and sound with the cheap piers. AND, the shed can be moved later if you desire.