I've always covered my baby
Some bassinets have cloth around the sides. It's not safe considering SIDS (sudden infant death syndrome). Babies are safest in a crib by their self with nothing in it not even blanket
Either or is fine. I loan on keeping my baby in its crib in the nursery for naps during the day but in no room in a bassinet at nite that way changings and feedings are easier for the first month or so.
I got a playpen with a bassinet for when shes tiny, but have a crib for when shes a few months older. I did the playpen because I can take it on trips, and she can still use it when she gets older, I can have it in the living room or anywhere. A bassinet works for newborns for a short time, so in the long run I'd do a playpen with a bassinet option, don't have to get the big ol fancy ones either. I think I spent 60 on mine. And a crib that grows with your child is good as well.