sleeping arrangements for baby!

My son is 5 weeks old! He does this weird thing where he will gag like 4 times or so. Sometimes he will throw up, spit up or nothing will happen. So I'm a nervous wreck when it comes to sleeping... We have a co-sleeper that goes in the bed and a rock and play beside the bed. He loves sleeping on his belly and sleeps longer that way. So when he's in the co-sleeper in the bed I put him on his belly and he'll sleep for about 3 hours but every time after that he wakes up EVERY hour and anytime I try laying him down either in the co-sleeper or rock and play he wakes right up. I want to start putting him in his crib hoping that he will sleep better. So my questions are taking the gagging into consideration, would it be safe to have him sleep in his crib in his room on his belly? Or should I keep him close by and keep him in the bed or rock and play? I've never had this issue with my daughter. She was always and good sleeper and slept in her crib since she was a month old. So I'm not really sure what would be the best thing to do for my son!