DS was a tummy sleeper. I didn't really let him sleep that way until he could roll over so I know he had excellent head control ( and I was a paranoid 1st tim mummy ). There are those 'anti roll' pillows to keep thm on their backs, but DS HATED his.
I have found DD likes being on her belly aswell... I have a feeling I will be where you are in a few weeks time.
I have never used a monitor myself, but I have had both in my room next to my bed for at least the first 6 months.

All the best!