When my daughter was born, they just made sure she was crying and put her on my belly. My first reaction was to pull my shirt up so she could go skin to skin, and then my first thought was, "she's so WARM!" (I don't know why that was surprising). I was also really surprised by what she smelled like in those first few moments- she smelled like warm would smell, ha.
My next thought was that it really WAS a baby. My whole pregnancy I had no connection to her, really, because I had trouble believing anything was really in there, and I even said in my dazed state, 'It IS a baby" and my sister asked, "what were you expecting?" I replied, "I don't know, an alien or a fish or something?" which made everyone laugh.
We did a homebirth at my inlaws, and after her birth DH went to sleep (he'd been up more than 24 hrs) and I sat in the living room with my mom and sister and MIL for hours with my baby, naked except for her diaper and wrapped in a blanket, and just looked at her various parts and memorized what all of her looked like and talked over the birth. It was great to just sit here and talk over everything that happened, how I felt, what surprised me, the best and worst parts. It made it seem more real somehow?
I actually cried when we put clothes on her (the next day) because I loved looking at and touching my little naked baby.