I'm a neonatal icu nurse. What we tell parents is put them on their back, head turned to the side, and nothing else in the bed, no pillows or animals. Instead of a blanket, wrap him if you think he'll get cold, or put thicker clothes on. He can have tummy time when he's awake and you are there, like when he's in the living room with you.
If he spits up when he's in the crib, roll up a blanket and just prop up one side of him but not too much.