This is an interesting discussion. I used to sleep on my side. This rounds my shoulder. I felt this caused most of my posture issues (you can only do so much when you spend 7 hours rounding your shoulder and putting weight on it).
Like you, I had trouble sleeping on my back/front and would always wake up on my side anyway.
Now, I sleep with my chest on the bed and my hips on the side. I use a flattish pillow - this kinda works okay but I wake up with a sore back now and again.
I always find I get a bad neck after using a new pillow. Three or four days and it sorts itself out.
I slept in a memory foam bed once and that seemed okay but don’t know about the long term…