Hi S.! We just put our 2 1/2 yr old in his own bed and I was amazed at how well it went. There have been a couple of afternoons that I found him asleep on the floor but it's to be expected since he can get up to play when he couldnt before. He sleeps in a full-size bed that we put 3 bed rails on. I thought he might feel overwhelmed by the size but it doesnt seem to bother him. We have a little step stool so that he can get in and out on his own.
You might consider putting him into a regular twin bed but that is your call. We had great success with both of our boys and didnt see the need for a toddler bed - friends who had them say they dont hold up well and they quidkly ended up in a big bed anyway. One set of friends just put the mattress and box springs directly on the floor.
We have a consistent bedtime ritual and we tuck him in at night and tell him that he needs to stay in bed. Inevitably, there are a couple of nights a week that I check on him before bed and he's asleep in the bed with the light on, surrounded by toys.