DD used to wear PJs/Wondersuit or a Bodysuit to bed. On really cold nights, also lightweight grobag. The way we used to sleep in the first few weeks was with me lying on my back and her on top of me, belly to belly IYKWIM. She was covered with our doona. When she started to get too heavy for that (and I got more confident), I used to sleep on my side, and she was on her side, facing me (at boob level, cause that's where she usually fell asleep). My bent legs were under her and my arm above her. Again, she was covered with my doona, but I always had my arm on top of te doona to prevent it from moving up and my legs were under her, so she couldn't slide under the doona.
I don't know where you live, but even here in SE Queensland a singlet and nappy wouldn't be nearly enough for a baby to wear to bed. I would dress DD in the type of clothing that I would feel comfortable in. So if I'm wearing long sleeved PJs, then that's what she wears. For a very young baby, my midwife said the rule of thunb is: what you wear plus one layer. So if you wear long sleeved PJs, PJs and singlet for her.

Hope that helps, Sasa