Snoring is an indicator of some degree of obstruction in your airway during sleep - it does not tell you anything about what stage of sleep you might be entering. REM sleep usually occurs 90 to 110 minutes after you fall asleep.
Looking at your weight/height your BMI (body mass index) is around 34, which is in the obesity class-I range. With this BMI and snoring there is a possibility that you might have sleep apnoea. So consider evaluation by a physician who specialises in this area.